Import dataset into R from your directory Here is my directory
Diagnostic Graphs
day_t0_germ_model= lmer((t0_germ)^-1~precip*soil_root+(1|block), data= dataSG_seed_1st_germ_trt)
qqPlot(resid(day_t0_germ_model))
## 3 85
## 2 56
hist(resid(day_t0_germ_model))
shapiro.test(resid(day_t0_germ_model))
##
## Shapiro-Wilk normality test
##
## data: resid(day_t0_germ_model)
## W = 0.96991, p-value = 0.1514
Raw Statistical output
anova(day_t0_germ_model)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.0119463 0.0119463 1 50.215 3.5356 0.06587 .
## soil_root 0.0313006 0.0156503 2 50.655 4.6318 0.01421 *
## precip:soil_root 0.0045726 0.0022863 2 51.349 0.6766 0.51279
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(day_t0_germ_model, pairwise~soil_root)
## Warning in ref_grid(object, ...): There are unevaluated constants in the response formula
## Auto-detection of the response transformation may be incorrect
## NOTE: Results may be misleading due to involvement in interactions
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.195 0.0148 11.9 0.162 0.227
## S.B 0.140 0.0176 21.6 0.103 0.176
## L.R 0.195 0.0150 12.7 0.163 0.228
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.054728 0.0201 49.2 2.726 0.0236
## L.B - L.R -0.000469 0.0183 51.3 -0.026 0.9996
## S.B - L.R -0.055197 0.0204 50.1 -2.702 0.0250
##
## Results are averaged over the levels of: precip
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates
emmeans(day_t0_germ_model, pairwise~soil_root|precip)
## Warning in ref_grid(object, ...): There are unevaluated constants in the response formula
## Auto-detection of the response transformation may be incorrect
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.187 0.0186 24.8 0.1488 0.226
## S.B 0.111 0.0223 35.9 0.0656 0.156
## L.R 0.187 0.0168 19.7 0.1519 0.222
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.202 0.0202 29.5 0.1608 0.243
## S.B 0.169 0.0254 42.2 0.1178 0.220
## L.R 0.203 0.0225 34.9 0.1576 0.249
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.076424 0.0272 51.2 2.807 0.0190
## L.B - L.R 0.000133 0.0227 49.8 0.006 1.0000
## S.B - L.R -0.076292 0.0257 50.0 -2.964 0.0127
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.033031 0.0303 49.8 1.091 0.5241
## L.B - L.R -0.001071 0.0283 51.2 -0.038 0.9992
## S.B - L.R -0.034101 0.0325 51.9 -1.048 0.5504
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
| Df | Resid.Df | F.value | P.value | |
|---|---|---|---|---|
| precip | 1 | 50.22 | 3.54 | 0.066 |
| soil_root | 2 | 50.66 | 4.63 | 0.014 |
| precip:soil_root | 2 | 51.35 | 0.68 | 0.513 |
Graph for publication
## Warning: `funs()` is deprecated as of dplyr 0.8.0.
## Please use a list of either functions or lambdas:
##
## # Simple named list:
## list(mean = mean, median = median)
##
## # Auto named with `tibble::lst()`:
## tibble::lst(mean, median)
##
## # Using lambdas
## list(~ mean(., trim = .2), ~ median(., na.rm = TRUE))
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.
Diagnostic Graphs
dataSG_seed_1st_germ_pres=subset(dataSG_seed_1st_germ_trt, root_association =="B")
unique(dataSG_seed_1st_germ_pres$soil_root)
## [1] L.B S.B
## Levels: L.B S.B L.R S.R
nrow(dataSG_seed_1st_germ_pres)
## [1] 60
day_t0_germ_model_pres= lmer((t0_germ)^-1~precip*soil_root+(1|block), data= dataSG_seed_1st_germ_pres)
qqPlot(resid(day_t0_germ_model_pres))
## 85 24
## 33 6
hist(resid(day_t0_germ_model_pres))
shapiro.test(resid(day_t0_germ_model_pres))
##
## Shapiro-Wilk normality test
##
## data: resid(day_t0_germ_model_pres)
## W = 0.98241, p-value = 0.8234
Raw Statistical output
anova(day_t0_germ_model_pres)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.0122308 0.0122308 1 29.562 4.2813 0.047376 *
## soil_root 0.0252094 0.0252094 1 28.581 8.8243 0.005968 **
## precip:soil_root 0.0052936 0.0052936 1 30.328 1.8530 0.183466
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(day_t0_germ_model_pres, pairwise~soil_root)
## Warning in ref_grid(object, ...): There are unevaluated constants in the response formula
## Auto-detection of the response transformation may be incorrect
## NOTE: Results may be misleading due to involvement in interactions
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.196 0.0168 5.72 0.1546 0.238
## S.B 0.141 0.0188 9.08 0.0987 0.184
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.0548 0.0185 28.2 2.966 0.0061
##
## Results are averaged over the levels of: precip
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
emmeans(day_t0_germ_model_pres, pairwise~soil_root|precip)
## Warning in ref_grid(object, ...): There are unevaluated constants in the response formula
## Auto-detection of the response transformation may be incorrect
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.190 0.0197 10.4 0.1459 0.233
## S.B 0.109 0.0227 15.8 0.0607 0.157
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.203 0.0211 12.6 0.1569 0.248
## S.B 0.174 0.0256 19.9 0.1201 0.227
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.0807 0.0255 29.9 3.161 0.0036
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.0290 0.0280 28.7 1.033 0.3103
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
Formatted Anova table
| Df | Resid.Df | F.value | P.value | |
|---|---|---|---|---|
| precip | 1 | 29.56 | 4.28 | 0.047 |
| soil_root | 1 | 28.58 | 8.82 | 0.006 |
| precip:soil_root | 1 | 30.33 | 1.85 | 0.183 |
Diagnostic Graphs
dataSG_seed_1st_germ_orig=subset(dataSG_seed_1st_germ_trt, soil_status =="L")
unique(dataSG_seed_1st_germ_orig$soil_root)
## [1] L.R L.B
## Levels: L.B S.B L.R S.R
nrow(dataSG_seed_1st_germ_orig)
## [1] 60
#60
day_t0_germ_model_orig= lmer((t0_germ)^-2~precip*soil_root+(1|block), data= dataSG_seed_1st_germ_orig)
qqPlot(resid(day_t0_germ_model_orig))
## 3 66
## 2 37
hist(resid(day_t0_germ_model_orig))
shapiro.test(resid(day_t0_germ_model_orig))
##
## Shapiro-Wilk normality test
##
## data: resid(day_t0_germ_model_orig)
## W = 0.93385, p-value = 0.01286
#0.01286
Raw Statistical output
anova(day_t0_germ_model_orig)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.00040305 0.00040305 1 39.847 1.0708 0.3070
## soil_root 0.00001075 0.00001075 1 40.258 0.0285 0.8667
## precip:soil_root 0.00000263 0.00000263 1 38.791 0.0070 0.9339
#emmeans(day_t0_germ_model_orig, pairwise~soil_root)
#emmeans(day_t0_germ_model_orig, pairwise~soil_root|precip)
Formatted Anova table
| Df | Resid.Df | F.value | P.value | |
|---|---|---|---|---|
| precip | 1 | 39.85 | 1.07 | 0.307 |
| soil_root | 1 | 40.26 | 0.03 | 0.867 |
| precip:soil_root | 1 | 38.79 | 0.01 | 0.934 |
Diagnostic Graphs
#Total germination
#convert to percentages
fin_dataSG_seed_surv_trt_tot_seedling$prop_tot_num_germ=fin_dataSG_seed_surv_trt_tot_seedling$tot_num_germ/10
seed_germ_model= glmer.nb((tot_num_germ)~precip*soil_root+(1|block), data= fin_dataSG_seed_surv_trt_tot_seedling)
## Warning in theta.ml(Y, mu, weights = object@resp$weights, limit = limit, :
## iteration limit reached
## boundary (singular) fit: see ?isSingular
qqPlot(resid(seed_germ_model))
## 37 42
## 59 61
hist(resid(seed_germ_model))
shapiro.test(resid(seed_germ_model))
##
## Shapiro-Wilk normality test
##
## data: resid(seed_germ_model)
## W = 0.93147, p-value = 0.0001422
#p-value = 0.0001422
plot(seed_germ_model)
#Chad's code for checking for over dispersion
overdisp_fun <- function(model) {
vpars <- function(m) {
nrow(m)*(nrow(m)+1)/2
}
model.df <- sum(sapply(VarCorr(model),vpars))+length(fixef(model))
rdf <- nrow(model.frame(model))-model.df
rp <- residuals(model,type="pearson")
Pearson.chisq <- sum(rp^2)
prat <- Pearson.chisq/rdf
pval <- pchisq(Pearson.chisq, df=rdf, lower.tail=FALSE)
c(chisq=Pearson.chisq,ratio=prat,rdf=rdf,p=pval)
}
overdisp_fun(seed_germ_model)
## chisq ratio rdf p
## 61.5017682 0.7409852 83.0000000 0.9629765
Raw Statistical output
summary(seed_germ_model)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Negative Binomial(54342.88) ( log )
## Formula: (tot_num_germ) ~ precip * soil_root + (1 | block)
## Data: fin_dataSG_seed_surv_trt_tot_seedling
##
## AIC BIC logLik deviance df.resid
## 222.9 242.9 -103.5 206.9 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.12545 -0.73029 -0.08396 0.40823 2.00830
##
## Random effects:
## Groups Name Variance Std.Dev.
## block (Intercept) 5.981e-11 7.733e-06
## Number of obs: 90, groups: block, 5
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.12688 0.11619 -1.092 0.2748
## precip1 0.24080 0.11618 2.073 0.0382 *
## soil_root1 0.21058 0.15408 1.367 0.1717
## soil_root2 -0.39015 0.17898 -2.180 0.0293 *
## precip1:soil_root1 -0.08811 0.15408 -0.572 0.5674
## precip1:soil_root2 -0.12923 0.17898 -0.722 0.4703
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) precp1 sl_rt1 sl_rt2 pr1:_1
## precip1 -0.211
## soil_root1 -0.178 0.072
## soil_root2 0.245 0.039 -0.556
## prcp1:sl_r1 0.072 -0.178 -0.185 0.027
## prcp1:sl_r2 0.039 0.245 0.027 -0.153 -0.556
## convergence code: 0
## boundary (singular) fit: see ?isSingular
Anova(seed_germ_model,type = 3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: (tot_num_germ)
## Chisq Df Pr(>Chisq)
## (Intercept) 1.1925 1 0.27483
## precip 4.2959 1 0.03821 *
## soil_root 4.7863 2 0.09134 .
## precip:soil_root 1.8911 2 0.38847
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(seed_germ_model,pairwise~soil_root|precip)
## $emmeans
## precip = A:
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 0.236 0.229 Inf -0.212 0.6849
## S.B -0.405 0.315 Inf -1.023 0.2119
## L.R 0.511 0.200 Inf 0.120 0.9021
##
## precip = D:
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B -0.069 0.267 Inf -0.592 0.4535
## S.B -0.629 0.352 Inf -1.318 0.0609
## L.R -0.405 0.315 Inf -1.023 0.2122
##
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df z.ratio p.value
## L.B - S.B 0.642 0.389 Inf 1.650 0.2248
## L.B - L.R -0.274 0.304 Inf -0.903 0.6381
## S.B - L.R -0.916 0.373 Inf -2.457 0.0373
##
## precip = D:
## contrast estimate SE df z.ratio p.value
## L.B - S.B 0.560 0.441 Inf 1.269 0.4126
## L.B - L.R 0.336 0.413 Inf 0.815 0.6938
## S.B - L.R -0.223 0.472 Inf -0.472 0.8843
##
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
| Df | Chi.Sq | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 1.19 | 0.275 |
| precip | 1 | 4.30 | 0.038 |
| soil_root | 2 | 4.79 | 0.091 |
| precip:soil_root | 2 | 1.89 | 0.388 |
Diagnostic Graphs
fin_dataSG_seed_surv_trt_tot_seedling_pres=subset(fin_dataSG_seed_surv_trt_tot_seedling, root_association =="B")
seed_germ_model_pres= glmer.nb((tot_num_germ)~precip*soil_root+(1|block), data= fin_dataSG_seed_surv_trt_tot_seedling_pres)
## Warning in theta.ml(Y, mu, weights = object@resp$weights, limit = limit, :
## iteration limit reached
qqPlot(resid(seed_germ_model_pres))
## 42 37
## 43 41
hist(resid(seed_germ_model_pres))
shapiro.test(resid(seed_germ_model_pres))
##
## Shapiro-Wilk normality test
##
## data: resid(seed_germ_model_pres)
## W = 0.92034, p-value = 0.0007916
#p-value = 0.0007916
plot(seed_germ_model_pres)
Raw Statistical output
summary(seed_germ_model_pres)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Negative Binomial(52724.35) ( log )
## Formula: (tot_num_germ) ~ precip * soil_root + (1 | block)
## Data: fin_dataSG_seed_surv_trt_tot_seedling_pres
##
## AIC BIC logLik deviance df.resid
## 146.5 159.1 -67.3 134.5 54
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.14275 -0.76619 -0.07703 0.58158 1.95560
##
## Random effects:
## Groups Name Variance Std.Dev.
## block (Intercept) 0.03097 0.176
## Number of obs: 60, groups: block, 5
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.23211 0.17146 -1.354 0.1758
## precip1 0.13213 0.14743 0.896 0.3701
## soil_root1 0.30036 0.14750 2.036 0.0417 *
## precip1:soil_root1 0.02056 0.14753 0.139 0.8892
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) precp1 sl_rt1
## precip1 -0.106
## soil_root1 -0.246 0.018
## prcp1:sl_r1 0.015 -0.289 -0.126
Anova(seed_germ_model_pres,type = 3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: (tot_num_germ)
## Chisq Df Pr(>Chisq)
## (Intercept) 1.8325 1 0.17583
## precip 0.8033 1 0.37012
## soil_root 4.1466 1 0.04172 *
## precip:soil_root 0.0194 1 0.88918
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(seed_germ_model_pres,pairwise~soil_root|precip)
## $emmeans
## precip = A:
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 0.2209 0.246 Inf -0.261 0.7024
## S.B -0.4209 0.327 Inf -1.063 0.2210
##
## precip = D:
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B -0.0844 0.281 Inf -0.635 0.4664
## S.B -0.6440 0.363 Inf -1.356 0.0681
##
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df z.ratio p.value
## L.B - S.B 0.642 0.390 Inf 1.645 0.0999
##
## precip = D:
## contrast estimate SE df z.ratio p.value
## L.B - S.B 0.560 0.443 Inf 1.264 0.2062
##
## Results are given on the log (not the response) scale.
Formatted Anova table
| Df | Chi.Sq | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 1.83 | 0.176 |
| precip | 1 | 0.80 | 0.370 |
| soil_root | 1 | 4.15 | 0.042 |
| precip:soil_root | 1 | 0.02 | 0.889 |
Diagnostic Graphs
fin_dataSG_seed_surv_trt_tot_seedling_org=subset(fin_dataSG_seed_surv_trt_tot_seedling, soil_status =="L")
seed_germ_model_org= glmer.nb((tot_num_germ)~precip*soil_root+(1|block), data= fin_dataSG_seed_surv_trt_tot_seedling_org)
## Warning in theta.ml(Y, mu, weights = object@resp$weights, limit = limit, :
## iteration limit reached
## boundary (singular) fit: see ?isSingular
qqPlot(resid(seed_germ_model_org))
## 58 6
## 49 26
hist(resid(seed_germ_model_org))
shapiro.test(resid(seed_germ_model_org))
##
## Shapiro-Wilk normality test
##
## data: resid(seed_germ_model_org)
## W = 0.95425, p-value = 0.02477
#p-value = 0.02477
plot(seed_germ_model_org)
Raw Statistical output
summary(seed_germ_model_org)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Negative Binomial(77187.13) ( log )
## Formula: (tot_num_germ) ~ precip * soil_root + (1 | block)
## Data: fin_dataSG_seed_surv_trt_tot_seedling_org
##
## AIC BIC logLik deviance df.resid
## 159.2 171.8 -73.6 147.2 54
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.12545 -0.59142 0.06902 0.40825 1.80738
##
## Random effects:
## Groups Name Variance Std.Dev.
## block (Intercept) 0 0
## Number of obs: 60, groups: block, 5
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.06818 0.12820 0.532 0.5948
## precip1 0.30542 0.12820 2.382 0.0172 *
## soil_root1 0.01551 0.12820 0.121 0.9037
## precip1:soil_root1 -0.15272 0.12820 -1.191 0.2335
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) precp1 sl_rt1
## precip1 -0.297
## soil_root1 -0.064 0.158
## prcp1:sl_r1 0.158 -0.064 -0.297
## convergence code: 0
## boundary (singular) fit: see ?isSingular
Anova(seed_germ_model_org,type = 3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: (tot_num_germ)
## Chisq Df Pr(>Chisq)
## (Intercept) 0.2829 1 0.5948
## precip 5.6755 1 0.0172 *
## soil_root 0.0146 1 0.9037
## precip:soil_root 1.4191 1 0.2335
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(seed_germ_model_org,pairwise~soil_root|precip)
## $emmeans
## precip = A:
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 0.236 0.229 Inf -0.213 0.685
## L.R 0.511 0.200 Inf 0.119 0.903
##
## precip = D:
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B -0.069 0.266 Inf -0.590 0.452
## L.R -0.405 0.316 Inf -1.025 0.214
##
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df z.ratio p.value
## L.B - L.R -0.274 0.304 Inf -0.902 0.3668
##
## precip = D:
## contrast estimate SE df z.ratio p.value
## L.B - L.R 0.336 0.413 Inf 0.815 0.4152
##
## Results are given on the log (not the response) scale.
Formatted Anova table
| Df | Chi.Sq | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 0.28 | 0.59 |
| precip | 1 | 5.68 | 0.02 |
| soil_root | 1 | 0.01 | 0.90 |
| precip:soil_root | 1 | 1.42 | 0.23 |
Graph for publication
## Warning: package 'gdtools' was built under R version 4.0.2
Diagnostic Graphs
seed_surv_germ_model= glmer(surv_germ~precip*soil_root+(1|block), data= fin_dataSG_biomass_seed_surv_trt_w_germ, family="binomial")
qqPlot(resid(seed_surv_germ_model))
## 24 71
## 14 47
hist(resid(seed_surv_germ_model))
shapiro.test(resid(seed_surv_germ_model))
##
## Shapiro-Wilk normality test
##
## data: resid(seed_surv_germ_model)
## W = 0.79433, p-value = 1.174e-07
#1.174e-07
plot(seed_surv_germ_model)
Raw Statistical output
Anova(seed_surv_germ_model, type=3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: surv_germ
## Chisq Df Pr(>Chisq)
## (Intercept) 4.6354 1 0.03132 *
## precip 0.0623 1 0.80290
## soil_root 7.0596 2 0.02931 *
## precip:soil_root 2.3638 2 0.30669
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#soil_root 9.8880 2 0.007126 **
#soil_root 7.0596 2 0.02931 *
#precip:soil_root 4.3070 2 0.116077
emmeans(seed_surv_germ_model, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 1.946 0.813 Inf 0.353 3.54
## S.B -0.243 0.746 Inf -1.705 1.22
## L.R 2.015 0.850 Inf 0.350 3.68
##
## Results are averaged over the levels of: precip
## Results are given on the logit (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df z.ratio p.value
## L.B - S.B 2.1897 0.942 Inf 2.324 0.0526
## L.B - L.R -0.0682 0.977 Inf -0.070 0.9973
## S.B - L.R -2.2579 0.996 Inf -2.266 0.0606
##
## Results are averaged over the levels of: precip
## Results are given on the log odds ratio (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
emmeans(seed_surv_germ_model, pairwise~soil_root|precip)
## $emmeans
## precip = A:
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 1.644 0.928 Inf -0.1741 3.462
## S.B 0.731 0.929 Inf -1.0904 2.552
## L.R 1.629 0.846 Inf -0.0287 3.287
##
## precip = D:
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 2.249 1.187 Inf -0.0779 4.576
## S.B -1.217 1.087 Inf -3.3480 0.913
## L.R 2.400 1.270 Inf -0.0886 4.888
##
## Results are given on the logit (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df z.ratio p.value
## L.B - S.B 0.9133 1.16 Inf 0.787 0.7110
## L.B - L.R 0.0146 1.08 Inf 0.013 0.9999
## S.B - L.R -0.8987 1.06 Inf -0.845 0.6748
##
## precip = D:
## contrast estimate SE df z.ratio p.value
## L.B - S.B 3.4662 1.53 Inf 2.259 0.0617
## L.B - L.R -0.1510 1.59 Inf -0.095 0.9951
## S.B - L.R -3.6172 1.67 Inf -2.168 0.0767
##
## Results are given on the log odds ratio (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
| Df | Chi.Sq | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 4.64 | 0.031 |
| precip | 1 | 0.06 | 0.803 |
| soil_root | 2 | 7.06 | 0.029 |
| precip:soil_root | 2 | 2.36 | 0.307 |
| Graph for publicati | on | ||
| <img src="MERDS_R_c | ode_SG | _reAnalysi | s_20200828_files/figure-html/unnamed-chunk-29-1.png" width=“672” /> |
Diagnostic Graphs
fin_dataSG_biomass_seed_surv_pres_w_germ=subset(fin_dataSG_biomass_seed_surv_trt_w_germ, root_association =="B")
seed_surv_germ_model_pres= glmer(surv_germ~precip*soil_root+(1|block), data= fin_dataSG_biomass_seed_surv_pres_w_germ, family="binomial")
## boundary (singular) fit: see ?isSingular
qqPlot(resid(seed_surv_germ_model_pres))
## 24 71
## 6 24
hist(resid(seed_surv_germ_model_pres))
shapiro.test(resid(seed_surv_germ_model_pres))
##
## Shapiro-Wilk normality test
##
## data: resid(seed_surv_germ_model_pres)
## W = 0.81516, p-value = 3.305e-05
#3.305e-05
plot(seed_surv_germ_model_pres)
Raw Statistical output
Anova(seed_surv_germ_model_pres, type=3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: surv_germ
## Chisq Df Pr(>Chisq)
## (Intercept) 4.3867 1 0.03622 *
## precip 0.1268 1 0.72178
## soil_root 5.3138 1 0.02116 *
## precip:soil_root 1.0721 1 0.30047
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(seed_surv_germ_model_pres, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 1.9033 0.654 Inf 0.621 3.19
## S.B -0.0912 0.566 Inf -1.201 1.02
##
## Results are averaged over the levels of: precip
## Results are given on the logit (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df z.ratio p.value
## L.B - S.B 1.99 0.865 Inf 2.305 0.0212
##
## Results are averaged over the levels of: precip
## Results are given on the log odds ratio (not the response) scale.
emmeans(seed_surv_germ_model_pres, pairwise~soil_root|precip)
## $emmeans
## precip = A:
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 1.609 0.775 Inf 0.0913 3.13
## S.B 0.511 0.730 Inf -0.9205 1.94
##
## precip = D:
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 2.197 1.054 Inf 0.1312 4.26
## S.B -0.693 0.866 Inf -2.3905 1.00
##
## Results are given on the logit (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df z.ratio p.value
## L.B - S.B 1.10 1.06 Inf 1.032 0.3021
##
## precip = D:
## contrast estimate SE df z.ratio p.value
## L.B - S.B 2.89 1.36 Inf 2.119 0.0341
##
## Results are given on the log odds ratio (not the response) scale.
Formatted Anova table
| Df | Chi.Sq | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 4.39 | 0.036 |
| precip | 1 | 0.13 | 0.722 |
| soil_root | 1 | 5.31 | 0.021 |
| precip:soil_root | 1 | 1.07 | 0.300 |
Diagnostic Graphs
fin_dataSG_biomass_seed_surv_orig_w_germ=subset(fin_dataSG_biomass_seed_surv_trt_w_germ, soil_status =="L")
seed_surv_germ_model_orig= glmer(surv_germ~precip*soil_root+(1|block), data= fin_dataSG_biomass_seed_surv_orig_w_germ, family="binomial")
qqPlot(resid(seed_surv_germ_model_orig))
## 24 71
## 14 41
hist(resid(seed_surv_germ_model_orig))
shapiro.test(resid(seed_surv_germ_model_orig))
##
## Shapiro-Wilk normality test
##
## data: resid(seed_surv_germ_model_orig)
## W = 0.54238, p-value = 1.23e-10
#1.23e-10
plot(seed_surv_germ_model_orig)
Raw Statistical output
Anova(seed_surv_germ_model_orig, type=3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: surv_germ
## Chisq Df Pr(>Chisq)
## (Intercept) 11.8503 1 0.0005765 ***
## precip 0.3965 1 0.5288941
## soil_root 0.0390 1 0.8433818
## precip:soil_root 0.0001 1 0.9942924
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(seed_surv_germ_model_orig, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 1.92 0.700 Inf 0.551 3.30
## L.R 1.74 0.714 Inf 0.341 3.14
##
## Results are averaged over the levels of: precip
## Results are given on the logit (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df z.ratio p.value
## L.B - L.R 0.184 0.931 Inf 0.198 0.8434
##
## Results are averaged over the levels of: precip
## Results are given on the log odds ratio (not the response) scale.
emmeans(seed_surv_germ_model_orig, pairwise~soil_root|precip)
## $emmeans
## precip = A:
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 1.63 0.819 Inf 0.0263 3.24
## L.R 1.45 0.724 Inf 0.0350 2.87
##
## precip = D:
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 2.22 1.086 Inf 0.0865 4.34
## L.R 2.03 1.139 Inf -0.2070 4.26
##
## Results are given on the logit (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df z.ratio p.value
## L.B - L.R 0.177 1.03 Inf 0.172 0.8634
##
## precip = D:
## contrast estimate SE df z.ratio p.value
## L.B - L.R 0.190 1.53 Inf 0.125 0.9009
##
## Results are given on the log odds ratio (not the response) scale.
Formatted Anova table
| Df | Chi.Sq | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 11.85 | 0.001 |
| precip | 1 | 0.40 | 0.529 |
| soil_root | 1 | 0.04 | 0.843 |
| precip:soil_root | 1 | 0.00 | 0.994 |
Diagnostic Graphs
seed_biomas_model= lmer(log(total_biomass)~precip*soil_root+(1|block), data= fin_dataSG_biomass_seed_surv_trt_given_germ)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(seed_biomas_model))
## 12 52
## 6 23
hist(resid(seed_biomas_model))
shapiro.test(resid(seed_biomas_model))
##
## Shapiro-Wilk normality test
##
## data: resid(seed_biomas_model)
## W = 0.9757, p-value = 0.457
#p-value = 0.457
Raw Statistical output
anova(seed_biomas_model)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.7614 0.7614 1 39 0.8395 0.3651603
## soil_root 7.2196 3.6098 2 39 3.9802 0.0267300 *
## precip:soil_root 18.1525 9.0763 2 39 10.0075 0.0003104 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(seed_biomas_model, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B -3.03 0.222 14.6 -3.51 -2.555
## S.B -1.76 0.427 28.4 -2.63 -0.885
## L.R -2.85 0.237 14.2 -3.36 -2.342
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B -1.271 0.475 38.9 -2.677 0.0285
## L.B - L.R -0.181 0.322 37.5 -0.563 0.8404
## S.B - L.R 1.089 0.495 38.0 2.201 0.0839
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
emmeans(seed_biomas_model, pairwise~soil_root|precip)
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B -2.639 0.309 28.4 -3.27 -2.01
## S.B -3.184 0.435 37.2 -4.07 -2.30
## L.R -2.281 0.278 25.8 -2.85 -1.71
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B -3.421 0.323 31.2 -4.08 -2.76
## S.B -0.335 0.740 32.3 -1.84 1.17
## L.R -3.417 0.379 30.9 -4.19 -2.64
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.54492 0.538 38.0 1.014 0.5729
## L.B - L.R -0.35848 0.413 36.5 -0.868 0.6635
## S.B - L.R -0.90339 0.511 36.3 -1.767 0.1951
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -3.08610 0.807 37.8 -3.822 0.0014
## L.B - L.R -0.00398 0.488 37.1 -0.008 1.0000
## S.B - L.R 3.08212 0.863 32.0 3.572 0.0032
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 39 | 0.84 | 0.365 |
| 2 | 39 | 3.98 | 0.027 |
| 2 | 39 | 10.01 | 0.000 |
| Graph | for publicat | ion | |
| <img s | rc="MERDS_R_ | code_SG_reA | nalysis_20200828_files/figure-html/unnamed-chunk-40-1.png" width=“672” /> |
Diagnostic Graphs
fin_dataSG_biomass_seed_surv_pres_w_germ=subset(fin_dataSG_biomass_seed_surv_trt_given_germ, root_association =="B")
nrow(fin_dataSG_biomass_seed_surv_pres_w_germ)
## [1] 26
#26
unique(fin_dataSG_biomass_seed_surv_pres_w_germ$soil_root)
## [1] L.B S.B
## Levels: L.B S.B L.R S.R
seed_biomas_model_pres= lmer((total_biomass)~precip*soil_root+(1|block), data= fin_dataSG_biomass_seed_surv_pres_w_germ)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(seed_biomas_model_pres))
## 25 75
## 6 21
hist(resid(seed_biomas_model_pres))
shapiro.test(resid(seed_biomas_model_pres))
##
## Shapiro-Wilk normality test
##
## data: resid(seed_biomas_model_pres)
## W = 0.93832, p-value = 0.1224
#p-value = 0.1224
Raw Statistical output
anova(seed_biomas_model_pres)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.43448 0.43448 1 22 147.58 3.139e-11 ***
## soil_root 0.44799 0.44799 1 22 152.17 2.336e-11 ***
## precip:soil_root 0.55107 0.55107 1 22 187.19 3.080e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(seed_biomas_model_pres, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.0664 0.0129 5.22 0.0338 0.099
## S.B 0.3859 0.0262 12.75 0.3291 0.443
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B -0.319 0.0284 21.9 -11.252 <.0001
##
## Results are averaged over the levels of: precip
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
emmeans(seed_biomas_model_pres, pairwise~soil_root|precip)
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.0863 0.0180 12.8 0.047359 0.1252
## S.B 0.0514 0.0251 20.1 -0.000969 0.1038
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.0466 0.0187 14.8 0.006715 0.0864
## S.B 0.7203 0.0466 15.7 0.621443 0.8192
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.0348 0.0313 20.9 1.114 0.2780
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -0.6737 0.0501 20.7 -13.448 <.0001
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 22 | 147.58 | 0 |
| 1 | 22 | 152.17 | 0 |
| 1 | 22 | 187.19 | 0 |
| ### Or | igin total b | iomass of g | erminated |
Diagnostic Graphs
fin_dataSG_biomass_seed_surv_orig_w_germ=subset(fin_dataSG_biomass_seed_surv_trt_given_germ, soil_status =="L")
nrow(fin_dataSG_biomass_seed_surv_orig_w_germ)
## [1] 38
#38
unique(fin_dataSG_biomass_seed_surv_orig_w_germ$soil_root)
## [1] L.R L.B
## Levels: L.B S.B L.R S.R
seed_biomas_model_orig= lmer(log(total_biomass)~precip*soil_root+(1|block), data= fin_dataSG_biomass_seed_surv_orig_w_germ)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(seed_biomas_model_orig))
## 12 52
## 6 21
hist(resid(seed_biomas_model_orig))
shapiro.test(resid(seed_biomas_model_orig))
##
## Shapiro-Wilk normality test
##
## data: resid(seed_biomas_model_orig)
## W = 0.97636, p-value = 0.5891
#p-value = 0.5891
Raw Statistical output
anova(seed_biomas_model_orig)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 8.4164 8.4164 1 34 8.7072 0.005705 **
## soil_root 0.3004 0.3004 1 34 0.3108 0.580839
## precip:soil_root 0.2874 0.2874 1 34 0.2973 0.589143
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(seed_biomas_model_orig, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B -3.03 0.230 11.8 -3.53 -2.53
## L.R -2.85 0.246 11.4 -3.39 -2.31
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - L.R -0.181 0.333 32.4 -0.544 0.5901
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
emmeans(seed_biomas_model_orig, pairwise~soil_root|precip)
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B -2.64 0.320 24.0 -3.30 -1.98
## L.R -2.28 0.288 21.6 -2.88 -1.68
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B -3.42 0.335 26.6 -4.11 -2.73
## L.R -3.42 0.393 26.3 -4.23 -2.61
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - L.R -0.35848 0.427 31.4 -0.840 0.4074
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - L.R -0.00398 0.505 32.1 -0.008 0.9938
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 34 | 8.71 | 0.006 |
| 1 | 34 | 0.31 | 0.581 |
| 1 | 34 | 0.30 | 0.589 |
Diagnostic Graphs
#now root:shoot ratio
fin_dataSG_biomass_seed_surv_trt_given_germ$root_shoot=fin_dataSG_biomass_seed_surv_trt_given_germ$root_weight_g/fin_dataSG_biomass_seed_surv_trt_given_germ$shoot_weight_g
summary(fin_dataSG_biomass_seed_surv_trt_given_germ)
## Plant_Number date Rdate exp_days
## Min. : 2.00 Length:45 Length:45 Min. :27
## 1st Qu.:23.00 Class :character Class :character 1st Qu.:27
## Median :52.00 Mode :character Mode :character Median :27
## Mean :46.49 Mean :27
## 3rd Qu.:66.00 3rd Qu.:27
## Max. :89.00 Max. :27
## num_germinates volunteer_dicot num_removed raw_label
## Min. :0.0000 Min. :0 Min. :0 Length:45
## 1st Qu.:1.0000 1st Qu.:0 1st Qu.:0 Class :character
## Median :1.0000 Median :0 Median :0 Mode :character
## Mean :0.9778 Mean :0 Mean :0
## 3rd Qu.:1.0000 3rd Qu.:0 3rd Qu.:0
## Max. :1.0000 Max. :0 Max. :0
## soil_status root_association block precip
## Length:45 Length:45 Min. :1.000 Length:45
## Class :character Class :character 1st Qu.:2.000 Class :character
## Mode :character Mode :character Median :3.000 Mode :character
## Mean :3.156
## 3rd Qu.:4.000
## Max. :5.000
## life_stage trt pot_w_germ soil_root
## Length:45 Length:45 Min. :0.0000 L.B:19
## Class :character Class :character 1st Qu.:1.0000 S.B: 7
## Mode :character Mode :character Median :1.0000 L.R:19
## Mean :0.9778 S.R: 0
## 3rd Qu.:1.0000
## Max. :1.0000
## tot_num_germ_harvest t0_germ germinated root_weight_g
## Min. :0.000 Min. : 4.000 Min. :1 Min. :0.0021
## 1st Qu.:1.000 1st Qu.: 4.000 1st Qu.:1 1st Qu.:0.0243
## Median :1.000 Median : 5.000 Median :1 Median :0.0507
## Mean :1.556 Mean : 6.044 Mean :1 Mean :0.1223
## 3rd Qu.:2.000 3rd Qu.: 6.000 3rd Qu.:1 3rd Qu.:0.1022
## Max. :4.000 Max. :19.000 Max. :1 Max. :1.1619
## shoot_weight_g total_biomass notes_roots notes_shoots
## Min. :0.00050 Min. :0.0026 Length:45 Length:45
## 1st Qu.:0.00360 1st Qu.:0.0294 Class :character Class :character
## Median :0.00640 Median :0.0612 Mode :character Mode :character
## Mean :0.00812 Mean :0.1305
## 3rd Qu.:0.01130 3rd Qu.:0.1116
## Max. :0.02560 Max. :1.1875
## sandy_root surv_germ root_shoot
## Length:45 Min. :1 Min. : 2.303
## Class :character 1st Qu.:1 1st Qu.: 4.168
## Mode :character Median :1 Median : 7.306
## Mean :1 Mean :14.315
## 3rd Qu.:1 3rd Qu.:13.850
## Max. :1 Max. :80.657
root_shoot_seed_model= lmer(log(root_shoot)~precip*soil_root+(1|block), data= fin_dataSG_biomass_seed_surv_trt_given_germ)
qqPlot(resid(root_shoot_seed_model))
## 51 52
## 22 23
hist(resid(root_shoot_seed_model))
shapiro.test(resid(root_shoot_seed_model))
##
## Shapiro-Wilk normality test
##
## data: resid(root_shoot_seed_model)
## W = 0.97031, p-value = 0.2972
#0.2972
Raw Statistical output
anova(root_shoot_seed_model, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 6.3079 6.3079 1 37.122 8.3663 0.006359 **
## soil_root 1.4238 0.7119 2 37.992 0.9442 0.397931
## precip:soil_root 3.9101 1.9550 2 38.417 2.5930 0.087835 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(root_shoot_seed_model, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 2.06 0.229 10.5 1.55 2.57
## S.B 2.56 0.406 28.2 1.73 3.39
## L.R 2.35 0.240 11.1 1.83 2.88
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B -0.504 0.432 38.0 -1.165 0.4808
## L.B - L.R -0.293 0.293 36.5 -1.002 0.5802
## S.B - L.R 0.211 0.451 39.0 0.467 0.8869
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
emmeans(root_shoot_seed_model, pairwise~soil_root|precip)
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 2.00 0.300 22.1 1.382 2.63
## S.B 1.54 0.412 34.2 0.701 2.37
## L.R 2.08 0.276 18.5 1.506 2.66
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 2.11 0.313 24.7 1.469 2.76
## S.B 3.59 0.683 36.3 2.203 4.97
## L.R 2.62 0.359 28.2 1.887 3.36
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.4664 0.487 36.8 0.957 0.6082
## L.B - L.R -0.0791 0.375 35.8 -0.211 0.9758
## S.B - L.R -0.5455 0.466 35.8 -1.171 0.4779
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -1.4742 0.734 39.0 -2.010 0.1233
## L.B - L.R -0.5076 0.445 36.4 -1.141 0.4954
## S.B - L.R 0.9666 0.783 38.4 1.235 0.4403
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 37.12 | 8.37 | 0.006 |
| 2 | 37.99 | 0.94 | 0.398 |
| 2 | 38.42 | 2.59 | 0.088 |
Graph for publication
Diagnostic Graphs
#now root:shoot ratio
fin_dataSG_biomass_seed_surv_pres_w_germ=subset(fin_dataSG_biomass_seed_surv_trt_given_germ, root_association =="B")
root_shoot_seed_model_pres= lmer(log(root_shoot)~precip*soil_root+(1|block), data= fin_dataSG_biomass_seed_surv_pres_w_germ)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(root_shoot_seed_model_pres))
## 20 75
## 2 21
hist(resid(root_shoot_seed_model_pres))
shapiro.test(resid(root_shoot_seed_model_pres))
##
## Shapiro-Wilk normality test
##
## data: resid(root_shoot_seed_model_pres)
## W = 0.97141, p-value = 0.6602
#0.6602
Raw Statistical output
anova(root_shoot_seed_model_pres, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 5.2766 5.2766 1 22 9.7046 0.005042 **
## soil_root 1.1572 1.1572 1 22 2.1283 0.158731
## precip:soil_root 4.8231 4.8231 1 22 8.8704 0.006934 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(root_shoot_seed_model_pres, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 2.08 0.175 5.22 1.64 2.52
## S.B 2.59 0.356 12.75 1.82 3.37
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B -0.513 0.386 21.9 -1.331 0.1970
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
emmeans(root_shoot_seed_model_pres, pairwise~soil_root|precip)
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 2.06 0.244 12.8 1.529 2.59
## S.B 1.52 0.341 20.1 0.811 2.23
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 2.11 0.254 14.8 1.564 2.65
## S.B 3.67 0.633 15.7 2.324 5.01
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.535 0.425 20.9 1.258 0.2224
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -1.562 0.681 20.7 -2.294 0.0324
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 22 | 9.70 | 0.005 |
| 1 | 22 | 2.13 | 0.159 |
| 1 | 22 | 8.87 | 0.007 |
| ### Or | igin Root:sh | oot ratio g | iven germination |
Diagnostic Graphs
#now root:shoot ratio
fin_dataSG_biomass_seed_surv_orig_w_germ=subset(fin_dataSG_biomass_seed_surv_trt_given_germ, soil_status =="L")
root_shoot_seed_model_orig= lmer(log(root_shoot)~precip*soil_root+(1|block), data= fin_dataSG_biomass_seed_surv_orig_w_germ)
qqPlot(resid(root_shoot_seed_model_orig))
## 51 52
## 20 21
hist(resid(root_shoot_seed_model_orig))
shapiro.test(resid(root_shoot_seed_model_orig))
##
## Shapiro-Wilk normality test
##
## data: resid(root_shoot_seed_model_orig)
## W = 0.96601, p-value = 0.2958
#0.2958
Raw Statistical output
anova(root_shoot_seed_model_orig, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.86205 0.86205 1 33.304 1.0003 0.3245
## soil_root 0.73422 0.73422 1 32.163 0.8519 0.3629
## precip:soil_root 0.41700 0.41700 1 31.393 0.4839 0.4918
emmeans(root_shoot_seed_model_orig, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 2.07 0.238 9.66 1.53 2.60
## L.R 2.35 0.250 10.07 1.79 2.91
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - L.R -0.285 0.314 31.8 -0.907 0.3711
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
emmeans(root_shoot_seed_model_orig, pairwise~soil_root|precip)
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 2.02 0.316 20.6 1.36 2.68
## L.R 2.09 0.289 17.5 1.48 2.70
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 2.11 0.330 23.0 1.43 2.80
## L.R 2.61 0.382 25.2 1.83 3.40
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - L.R -0.0709 0.402 31.0 -0.176 0.8612
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - L.R -0.4989 0.477 31.5 -1.046 0.3033
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 33.30 | 1.00 | 0.324 |
| 1 | 32.16 | 0.85 | 0.363 |
| 1 | 31.39 | 0.48 | 0.492 |
Diagnostic Graphs
SG_inorg_N_trt$soil_root=with(SG_inorg_N_trt, interaction(soil_status,root_association))
SG_inorg_N_seed_trt= subset(SG_inorg_N_trt, life_stage=="S")
SG_soil_nit_model= lmer((ug_N_NO3_g_dry_soil)~precip*soil_root+(1|block), data= SG_inorg_N_seed_trt)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(SG_soil_nit_model))
## [1] 1 2
hist(resid(SG_soil_nit_model))
shapiro.test(resid(SG_soil_nit_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_soil_nit_model)
## W = 0.95913, p-value = 0.7402
#0.7402
Raw Statistical output
anova(SG_soil_nit_model, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 11.4658 11.4658 1 7 38.967 0.0004273 ***
## soil_root 9.9131 4.9566 2 7 16.845 0.0021117 **
## precip:soil_root 8.8261 4.4131 2 7 14.998 0.0029466 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_soil_nit_model, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 5.98 0.344 7.00 5.17 6.80
## S.B 3.33 0.369 7.00 2.46 4.21
## L.R 4.68 0.257 5.49 4.04 5.32
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B 2.65 0.505 5.35 5.249 0.0064
## L.B - L.R 1.30 0.419 4.74 3.111 0.0621
## S.B - L.R -1.35 0.450 5.49 -2.991 0.0603
##
## Results are averaged over the levels of: precip
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates
emmeans(SG_soil_nit_model, pairwise~soil_root|precip)
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 3.57 0.344 7 2.76 4.38
## S.B 3.31 0.436 7 2.28 4.35
## L.R 3.91 0.271 7 3.27 4.55
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 8.40 0.690 7 6.77 10.03
## S.B 3.35 0.664 7 1.78 4.92
## L.R 5.45 0.436 7 4.42 6.48
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.254 0.571 6.37 0.445 0.8984
## L.B - L.R -0.339 0.438 4.82 -0.773 0.7346
## S.B - L.R -0.593 0.514 5.49 -1.153 0.5230
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 5.043 0.985 7.00 5.123 0.0034
## L.B - L.R 2.946 0.784 5.49 3.758 0.0254
## S.B - L.R -2.098 0.848 7.00 -2.475 0.0953
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 29.56 | 4.28 | 0.047 |
| 1 | 28.58 | 8.82 | 0.006 |
| 1 | 30.33 | 1.85 | 0.183 |
| Graph | for publicat | ion | |
| <img s | rc="MERDS_R_ | code_SG_reA | nalysis_20200828_files/figure-html/unnamed-chunk-60-1.png" width=“672” /> |
Diagnostic Graphs
SG_soil_amm_model= lmer((ug_N_NH4_g_dry_soil_negto0)~precip*soil_root+(1|block), data= SG_inorg_N_seed_trt)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(SG_soil_amm_model))
## [1] 12 13
hist(resid(SG_soil_amm_model))
shapiro.test(resid(SG_soil_amm_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_soil_amm_model)
## W = 0.60938, p-value = 7.899e-05
#p-value = 7.899e-05
Raw Statistical output
anova(SG_soil_amm_model, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.2271 0.22709 1 7 0.2559 0.6285
## soil_root 5.3807 2.69034 2 7 3.0317 0.1126
## precip:soil_root 0.0893 0.04463 2 7 0.0503 0.9513
emmeans(SG_soil_amm_model, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.131 0.597 7.00 -1.281 1.54
## S.B 1.851 0.641 7.00 0.335 3.37
## L.R 0.279 0.446 5.49 -0.837 1.40
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B -1.721 0.876 5.35 -1.964 0.2106
## L.B - L.R -0.148 0.728 4.74 -0.204 0.9774
## S.B - L.R 1.572 0.781 5.49 2.013 0.1966
##
## Results are averaged over the levels of: precip
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates
emmeans(SG_soil_amm_model, pairwise~soil_root|precip)
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.0406 0.597 7 -1.3716 1.45
## S.B 1.7611 0.758 7 -0.0307 3.55
## L.R 0.0088 0.471 7 -1.1050 1.12
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.2210 1.198 7 -2.6121 3.05
## S.B 1.9418 1.154 7 -0.7864 4.67
## L.R 0.5498 0.758 7 -1.2420 2.34
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -1.7205 0.992 6.37 -1.735 0.2644
## L.B - L.R 0.0318 0.761 4.82 0.042 0.9990
## S.B - L.R 1.7523 0.892 5.49 1.964 0.2085
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -1.7207 1.710 7.00 -1.006 0.5963
## L.B - L.R -0.3288 1.361 5.49 -0.242 0.9685
## S.B - L.R 1.3919 1.472 7.00 0.946 0.6310
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates
Graph for publication
## Warning: Removed 2 rows containing missing values (geom_text).
Was there treatment effects on intial survival
Graph Was there a bias in initial height?
Diagnostic Graphs
SG_intial_height_model= lmer((int_height_cm)^(1/3)~precip*soil_root+(1|block), data= fin_dataSG_trans_surv_trt_planting)
qqPlot(resid(SG_intial_height_model))
## [1] 14 7
hist(resid(SG_intial_height_model))
shapiro.test(resid(SG_intial_height_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_intial_height_model)
## W = 0.93125, p-value = 0.0001383
#p-value = 0.0001383
Raw Statistical output
anova(SG_intial_height_model)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.000081 0.0000813 1 80 0.0033 0.9546
## soil_root 0.044662 0.0223308 2 80 0.8961 0.4122
## precip:soil_root 0.060344 0.0301722 2 80 1.2108 0.3034
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 80 | 0.00 | 0.955 |
| 2 | 80 | 0.90 | 0.412 |
| 2 | 80 | 1.21 | 0.303 |
| ### To | tal biomass |
Diagnostic Graphs
trans_biomas_model= lmer(log(total_biomass_0+.001)~precip*soil_root+(1|block), data= data_SG_biomass_trans_surv_trt)
qqPlot(resid(trans_biomas_model))
## [1] 29 41
hist(resid(trans_biomas_model))
shapiro.test(resid(trans_biomas_model))
##
## Shapiro-Wilk normality test
##
## data: resid(trans_biomas_model)
## W = 0.96619, p-value = 0.01918
Raw Statistical output
anova(trans_biomas_model, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 31.948 31.948 1 80 13.4201 0.0004457 ***
## soil_root 23.301 11.651 2 80 4.8939 0.0098833 **
## precip:soil_root 15.880 7.940 2 80 3.3353 0.0406192 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(trans_biomas_model, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B -3.39 0.323 15.6 -4.08 -2.71
## S.B -2.48 0.323 15.6 -3.17 -1.80
## L.R -3.67 0.323 15.6 -4.36 -2.99
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log(mu + 0.001) (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B -0.909 0.398 80 -2.282 0.0641
## L.B - L.R 0.284 0.398 80 0.712 0.7570
## S.B - L.R 1.193 0.398 80 2.994 0.0101
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
emmeans(trans_biomas_model, pairwise~soil_root|precip)
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B -3.16 0.429 38.4 -4.03 -2.294
## S.B -1.30 0.429 38.4 -2.17 -0.431
## L.R -3.30 0.429 38.4 -4.17 -2.434
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B -3.62 0.429 38.4 -4.49 -2.754
## S.B -3.67 0.429 38.4 -4.53 -2.799
## L.R -4.05 0.429 38.4 -4.92 -3.181
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log(mu + 0.001) (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -1.8632 0.563 80 -3.307 0.0040
## L.B - L.R 0.1403 0.563 80 0.249 0.9664
## S.B - L.R 2.0036 0.563 80 3.556 0.0018
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.0449 0.563 80 0.080 0.9965
## L.B - L.R 0.4272 0.563 80 0.758 0.7295
## S.B - L.R 0.3823 0.563 80 0.678 0.7767
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 80 | 13.42 | 0.000 |
| 2 | 80 | 4.89 | 0.010 |
| 2 | 80 | 3.34 | 0.041 |
Graph for publication
Diagnostic Graphs
data_SG_biomass_trans_surv_pres=subset(data_SG_biomass_trans_surv_trt, root_association =="B")
trans_biomas_model_pres= lmer((total_biomass_0+.001)^(1/4)~precip*soil_root+(1|block), data= data_SG_biomass_trans_surv_pres)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(trans_biomas_model_pres))
## 85 34
## 55 19
hist(resid(trans_biomas_model_pres))
shapiro.test(resid(trans_biomas_model_pres))
##
## Shapiro-Wilk normality test
##
## data: resid(trans_biomas_model_pres)
## W = 0.97499, p-value = 0.254
#p-value = 0.254
Raw Statistical output
anova(trans_biomas_model_pres, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.38241 0.38241 1 56 13.2458 0.0005969 ***
## soil_root 0.29851 0.29851 1 56 10.3396 0.0021637 **
## precip:soil_root 0.25587 0.25587 1 56 8.8628 0.0042933 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(trans_biomas_model_pres, pairwise~soil_root)
## Warning in ref_grid(object, ...): There are unevaluated constants in the response formula
## Auto-detection of the response transformation may be incorrect
## NOTE: Results may be misleading due to involvement in interactions
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.455 0.031 14.9 0.389 0.521
## S.B 0.596 0.031 14.9 0.530 0.662
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B -0.141 0.0439 52 -3.216 0.0022
##
## Results are averaged over the levels of: precip
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
emmeans(trans_biomas_model_pres, pairwise~soil_root|precip)
## Warning in ref_grid(object, ...): There are unevaluated constants in the response formula
## Auto-detection of the response transformation may be incorrect
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.469 0.0439 37.8 0.380 0.558
## S.B 0.741 0.0439 37.8 0.652 0.830
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.440 0.0439 37.8 0.351 0.529
## S.B 0.451 0.0439 37.8 0.362 0.540
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -0.2717 0.062 52 -4.379 0.0001
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -0.0105 0.062 52 -0.169 0.8667
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 56 | 13.25 | 0.001 |
| 1 | 56 | 10.34 | 0.002 |
| 1 | 56 | 8.86 | 0.004 |
Diagnostic Graphs
data_SG_biomass_trans_surv_orig=subset(data_SG_biomass_trans_surv_trt, soil_status =="L")
nrow(data_SG_biomass_trans_surv_orig)
## [1] 60
trans_biomas_model_orig= lmer((total_biomass_0+0.001)^(1/4)~precip*soil_root+(1|block), data= data_SG_biomass_trans_surv_orig)
qqPlot(resid(trans_biomas_model_orig))
## [1] 2 29
hist(resid(trans_biomas_model_orig))
shapiro.test(resid(trans_biomas_model_orig))
##
## Shapiro-Wilk normality test
##
## data: resid(trans_biomas_model_orig)
## W = 0.97214, p-value = 0.1856
#p-value = 0.1856
Raw Statistical output
anova(trans_biomas_model_orig)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.0212028 0.0212028 1 52 1.0133 0.3188
## soil_root 0.0111201 0.0111201 1 52 0.5314 0.4693
## precip:soil_root 0.0010927 0.0010927 1 52 0.0522 0.8201
emmeans(trans_biomas_model_orig, pairwise~soil_root)
## Warning in ref_grid(object, ...): There are unevaluated constants in the response formula
## Auto-detection of the response transformation may be incorrect
## NOTE: Results may be misleading due to involvement in interactions
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.455 0.0313 9.4 0.384 0.525
## L.R 0.428 0.0313 9.4 0.357 0.498
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - L.R 0.0272 0.0373 52 0.729 0.4693
##
## Results are averaged over the levels of: precip
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
emmeans(trans_biomas_model_orig, pairwise~soil_root|precip)
## Warning in ref_grid(object, ...): There are unevaluated constants in the response formula
## Auto-detection of the response transformation may be incorrect
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.469 0.041 23.3 0.385 0.554
## L.R 0.451 0.041 23.3 0.366 0.535
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.440 0.041 23.3 0.356 0.525
## L.R 0.404 0.041 23.3 0.320 0.489
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - L.R 0.0187 0.0528 52 0.354 0.7249
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - L.R 0.0358 0.0528 52 0.677 0.5014
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 52 | 1.01 | 0.319 |
| 1 | 52 | 0.53 | 0.469 |
| 1 | 52 | 0.05 | 0.820 |
Diagnostic Graphs
root_shoot_model_na= lmer(log(root_shoot)~precip*soil_root+(1|block), data= data_SG_biomass_trans_surv_trt_na)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(root_shoot_model_na))
## 53 45
## 43 35
hist(resid(root_shoot_model_na))
shapiro.test(resid(root_shoot_model_na))
##
## Shapiro-Wilk normality test
##
## data: resid(root_shoot_model_na)
## W = 0.94233, p-value = 0.001287
#p-value = 0.001287
plot(root_shoot_model_na)
Raw Statistical output
anova(root_shoot_model_na)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 2.3613 2.36129 1 74 1.4419 0.2337
## soil_root 1.0009 0.50045 2 74 0.3056 0.7376
## precip:soil_root 1.5907 0.79534 2 74 0.4857 0.6172
emmeans(root_shoot_model_na, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 1.13 0.243 26.7 0.628 1.62
## S.B 1.03 0.255 29.7 0.511 1.55
## L.R 1.31 0.257 28.1 0.782 1.83
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.0942 0.352 70.7 0.267 0.9614
## L.B - L.R -0.1818 0.354 71.9 -0.514 0.8648
## S.B - L.R -0.2759 0.361 71.3 -0.765 0.7258
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
emmeans(root_shoot_model_na, pairwise~soil_root|precip)
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.814 0.330 54.4 0.152 1.48
## S.B 1.054 0.330 54.4 0.392 1.72
## L.R 1.077 0.330 54.4 0.415 1.74
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 1.438 0.356 58.5 0.726 2.15
## S.B 1.010 0.389 61.7 0.232 1.79
## L.R 1.539 0.393 56.9 0.752 2.33
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -0.2403 0.467 70.0 -0.514 0.8647
## L.B - L.R -0.2630 0.467 70.0 -0.563 0.8402
## S.B - L.R -0.0227 0.467 70.0 -0.049 0.9987
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.4286 0.527 71.2 0.814 0.6959
## L.B - L.R -0.1006 0.531 73.0 -0.189 0.9804
## S.B - L.R -0.5292 0.550 72.1 -0.962 0.6031
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 74 | 1.44 | 0.234 |
| 2 | 74 | 0.31 | 0.738 |
| 2 | 74 | 0.49 | 0.617 |
Graph for publication
Diagnostic Graphs
data_SG_biomass_trans_surv_pres_na=subset(data_SG_biomass_trans_surv_trt_na, root_association =="B")
root_shoot_model_pres_na= lmer((root_shoot)^(1/4)~precip*soil_root+(1|block), data= data_SG_biomass_trans_surv_pres_na)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(root_shoot_model_pres_na))
## 25 45
## 9 24
hist(resid(root_shoot_model_pres_na))
shapiro.test(resid(root_shoot_model_pres_na))
##
## Shapiro-Wilk normality test
##
## data: resid(root_shoot_model_pres_na)
## W = 0.94371, p-value = 0.01335
#p-value = 0.01335
plot(root_shoot_model_pres_na)
Raw Statistical output
anova(root_shoot_model_pres_na)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.175840 0.175840 1 50 1.1108 0.2970
## soil_root 0.009263 0.009263 1 50 0.0585 0.8099
## precip:soil_root 0.250414 0.250414 1 50 1.5818 0.2143
emmeans(root_shoot_model_pres_na, pairwise~soil_root)
## Warning in ref_grid(object, ...): There are unevaluated constants in the response formula
## Auto-detection of the response transformation may be incorrect
## NOTE: Results may be misleading due to involvement in interactions
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 1.38 0.0756 13.6 1.22 1.55
## S.B 1.36 0.0795 15.4 1.19 1.53
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.0264 0.11 46.7 0.241 0.8107
##
## Results are averaged over the levels of: precip
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
emmeans(root_shoot_model_pres_na, pairwise~soil_root|precip)
## Warning in ref_grid(object, ...): There are unevaluated constants in the response formula
## Auto-detection of the response transformation may be incorrect
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 1.26 0.103 32.5 1.05 1.47
## S.B 1.37 0.103 32.5 1.16 1.58
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 1.51 0.111 35.8 1.28 1.73
## S.B 1.35 0.121 38.5 1.10 1.59
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -0.111 0.145 46.0 -0.763 0.4492
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.164 0.164 47.2 0.997 0.3238
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 50 | 1.11 | 0.297 |
| 1 | 50 | 0.06 | 0.810 |
| 1 | 50 | 1.58 | 0.214 |
Diagnostic Graphs
data_SG_biomass_trans_surv_orig_na=subset(data_SG_biomass_trans_surv_trt_na,soil_status =="L")
root_shoot_model_orig_na= lmer(log(root_shoot)~precip*soil_root+(1|block), data= data_SG_biomass_trans_surv_orig_na)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(root_shoot_model_orig_na))
## 53 25
## 32 20
hist(resid(root_shoot_model_orig_na))
shapiro.test(resid(root_shoot_model_orig_na))
##
## Shapiro-Wilk normality test
##
## data: resid(root_shoot_model_orig_na)
## W = 0.94863, p-value = 0.02169
#p-value = 0.02169
plot(root_shoot_model_orig_na)
Raw Statistical output
anova(root_shoot_model_orig_na)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 3.9134 3.9134 1 50 2.4860 0.1212
## soil_root 0.4389 0.4389 1 50 0.2788 0.5998
## precip:soil_root 0.0875 0.0875 1 50 0.0556 0.8145
emmeans(root_shoot_model_orig_na, pairwise~soil_root|precip)
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.814 0.324 32.3 0.155 1.47
## L.R 1.077 0.324 32.3 0.417 1.74
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 1.438 0.350 35.6 0.729 2.15
## L.R 1.539 0.388 34.2 0.750 2.33
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - L.R -0.263 0.458 46 -0.574 0.5688
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - L.R -0.101 0.523 49 -0.192 0.8484
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 50 | 2.49 | 0.121 |
| 1 | 50 | 0.28 | 0.600 |
| 1 | 50 | 0.06 | 0.815 |
data_SG_biomass_trans_surv_trt$surv=data_SG_biomass_trans_surv_trt$total_biomass
data_SG_biomass_trans_surv_trt$surv[is.na(data_SG_biomass_trans_surv_trt$surv)]=0
data_SG_biomass_trans_surv_trt$surv[data_SG_biomass_trans_surv_trt$surv!=0]=1
Diagnostic Graphs
Raw Statistical output
Graph for publication
Final survival in the drought treatment only since all pots had live transs in the ambient treatments
Diagnostic Graphs
data_SG_biomass_trans_surv_drought=subset(data_SG_biomass_trans_surv_trt, precip=="D")
drought_surv_model= glmer(surv~soil_root+(1|block), data= data_SG_biomass_trans_surv_drought, family = binomial)
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0139762 (tol = 0.002, component 1)
qqPlot(resid(drought_surv_model))
## [1] 29 41
hist(resid(drought_surv_model))
Raw Statistical output
Anova(drought_surv_model,type = 3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: surv
## Chisq Df Pr(>Chisq)
## (Intercept) 88736 1 < 2.2e-16 ***
## soil_root 15916 2 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(drought_surv_model, pairwise~soil_root)
## $emmeans
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 2.15 0.00716 Inf 2.133 2.16
## S.B 1.19 0.44169 Inf 0.323 2.05
## L.R 1.19 0.44169 Inf 0.323 2.05
##
## Results are given on the logit (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df z.ratio p.value
## L.B - S.B 9.58e-01 0.442 Inf 2.168 0.0767
## L.B - L.R 9.58e-01 0.442 Inf 2.168 0.0767
## S.B - L.R 2.16e-05 0.883 Inf 0.000 1.0000
##
## Results are given on the log odds ratio (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
| Df | Chi.Sq | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 88735.85 | 0 |
| soil_root | 2 | 15916.28 | 0 |
Diagnostic Graphs
data_SG_biomass_trans_surv_drought_pres=subset(data_SG_biomass_trans_surv_drought, root_association =="B")
drought_surv_model_pres= glmer(surv~soil_root+(1|block), data= data_SG_biomass_trans_surv_drought_pres, family = binomial)
qqPlot(resid(drought_surv_model_pres))
## 29 16
## 14 1
hist(resid(drought_surv_model_pres))
Raw Statistical output
Anova(drought_surv_model_pres,type = 3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: surv
## Chisq Df Pr(>Chisq)
## (Intercept) 7.2643 1 0.007034 **
## soil_root 0.8025 1 0.370340
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(drought_surv_model_pres, pairwise~soil_root)
## $emmeans
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 1.89 0.815 Inf 0.288 3.48
## S.B 1.02 0.619 Inf -0.192 2.23
##
## Results are given on the logit (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df z.ratio p.value
## L.B - S.B 0.865 0.966 Inf 0.896 0.3703
##
## Results are given on the log odds ratio (not the response) scale.
Formatted Anova table
| Df | Chi.Sq | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 7.26 | 0.007 |
| soil_root | 1 | 0.80 | 0.370 |
Diagnostic Graphs
data_SG_biomass_trans_surv_drought_orig=subset(data_SG_biomass_trans_surv_drought, soil_status =="L")
drought_surv_model_orig= glmer(surv~soil_root+(1|block), data= data_SG_biomass_trans_surv_drought_orig, family = binomial)
qqPlot(resid(drought_surv_model_orig))
## [1] 29 16
hist(resid(drought_surv_model_orig))
Raw Statistical output
Anova(drought_surv_model_orig,type = 3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: surv
## Chisq Df Pr(>Chisq)
## (Intercept) 4.9500 1 0.02609 *
## soil_root 0.8716 1 0.35052
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(drought_surv_model_orig, pairwise~soil_root)
## $emmeans
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 2.12 0.996 Inf 0.173 4.08
## L.R 1.17 0.791 Inf -0.377 2.73
##
## Results are given on the logit (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df z.ratio p.value
## L.B - L.R 0.95 1.02 Inf 0.934 0.3505
##
## Results are given on the log odds ratio (not the response) scale.
Formatted Anova table
| Df | Chi.Sq | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 4.95 | 0.026 |
| soil_root | 1 | 0.87 | 0.351 |
Diagnostic Graphs
SRL_trans_model= lmer((SRL_length_drymass)~precip*soil_root+(1|block), data= SG_roottraits_trt)
qqPlot(resid(SRL_trans_model))
## [1] 18 8
hist(resid(SRL_trans_model))
shapiro.test(resid(SRL_trans_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SRL_trans_model)
## W = 0.97902, p-value = 0.8396
Raw Statistical output
anova(SRL_trans_model)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 119509598 119509598 1 18.017 5.5697 0.02975 *
## soil_root 33012605 16506303 2 17.454 0.7693 0.47843
## precip:soil_root 174500103 87250052 2 17.454 4.0663 0.03551 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SRL_trans_model, pairwise~soil_root|precip)
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 14406 2145 20.6 9939 18873
## S.B 10446 2145 20.6 5979 14913
## L.R 11348 2145 20.6 6882 15815
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 12476 2145 20.6 8009 16942
## S.B 21317 2844 21.0 15402 27232
## L.R 15338 2430 20.8 10282 20394
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 3960 2930 17.1 1.352 0.3872
## L.B - L.R 3058 2930 17.1 1.044 0.5604
## S.B - L.R -902 2930 17.1 -0.308 0.9492
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -8841 3474 18.2 -2.545 0.0504
## L.B - L.R -2862 3144 17.6 -0.910 0.6411
## S.B - L.R 5979 3593 17.7 1.664 0.2462
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 18.02 | 5.57 | 0.030 |
| 2 | 17.45 | 0.77 | 0.478 |
| 2 | 17.45 | 4.07 | 0.036 |
| Graph | for publicat | ion |
Diagnostic Graphs
SG_roottraits_pres=subset(SG_roottraits_trt, root_association =="B")
SRL_trans_model_pres= lmer((SRL_length_drymass)~precip*soil_root+(1|block), data= SG_roottraits_pres)
qqPlot(resid(SRL_trans_model_pres))
## 18 8
## 9 4
hist(resid(SRL_trans_model_pres))
shapiro.test(resid(SRL_trans_model_pres))
##
## Shapiro-Wilk normality test
##
## data: resid(SRL_trans_model_pres)
## W = 0.97446, p-value = 0.876
Raw Statistical output
anova(SRL_trans_model_pres)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 95886515 95886515 1 10.131 4.8407 0.05209 .
## soil_root 31805805 31805805 1 10.131 1.6057 0.23345
## precip:soil_root 188806702 188806702 1 10.131 9.5317 0.01133 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SRL_trans_model_pres, pairwise~soil_root|precip)
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 14406 2304 12.0 9387 19424
## S.B 10446 2304 12.0 5428 15464
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 12476 2304 12.0 7457 17494
## S.B 21949 2987 13.8 15532 28366
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 3960 2815 10.0 1.407 0.1897
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -9473 3397 10.8 -2.789 0.0180
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 10.13 | 4.84 | 0.052 |
| 1 | 10.13 | 1.61 | 0.233 |
| 1 | 10.13 | 9.53 | 0.011 |
Diagnostic Graphs
SG_roottraits_orig=subset(SG_roottraits_trt,soil_status =="L")
SRL_trans_model_orig= lmer((SRL_length_drymass)~precip*soil_root+(1|block), data= SG_roottraits_orig)
qqPlot(resid(SRL_trans_model_orig))
## 18 8
## 15 8
hist(resid(SRL_trans_model_orig))
shapiro.test(resid(SRL_trans_model_orig))
##
## Shapiro-Wilk normality test
##
## data: resid(SRL_trans_model_orig)
## W = 0.968, p-value = 0.7359
Raw Statistical output
anova(SRL_trans_model_orig)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 4777217 4777217 1 11.588 0.1724 0.6856
## soil_root 66735 66735 1 11.588 0.0024 0.9617
## precip:soil_root 40567718 40567718 1 11.588 1.4637 0.2504
emmeans(SRL_trans_model_orig, pairwise~soil_root|precip)
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 14406 2390 15 9312 19500
## L.R 11348 2390 15 6254 16443
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 12476 2390 15 7381 17570
## L.R 15295 2741 15 9452 21138
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - L.R 3058 3330 11.0 0.918 0.3781
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - L.R -2819 3590 11.6 -0.785 0.4480
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 11.59 | 0.17 | 0.686 |
| 1 | 11.59 | 0.00 | 0.962 |
| 1 | 11.59 | 1.46 | 0.250 |
Diagnostic Graphs
RLD_trans_model= lmer((RLD_length_volume)~precip*soil_root+(1|block), data= SG_roottraits_trt)
qqPlot(resid(RLD_trans_model))
## [1] 23 1
hist(resid(RLD_trans_model))
Raw Statistical output
anova(RLD_trans_model, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.4102 0.4102 1 16.865 5.0491 0.038322 *
## soil_root 6.3528 3.1764 2 16.061 39.0983 6.734e-07 ***
## precip:soil_root 1.2403 0.6201 2 16.061 7.6332 0.004677 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(RLD_trans_model, pairwise~soil_root|precip)
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.548 0.130 20.9 0.277 0.818
## S.B 2.071 0.130 20.9 1.801 2.342
## L.R 0.487 0.130 20.9 0.216 0.757
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.472 0.130 20.9 0.202 0.743
## S.B 1.195 0.173 21.0 0.835 1.555
## L.R 0.683 0.148 20.9 0.376 0.990
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -1.5238 0.180 17.1 -8.453 <.0001
## L.B - L.R 0.0609 0.180 17.1 0.338 0.9393
## S.B - L.R 1.5847 0.180 17.1 8.791 <.0001
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -0.7229 0.214 18.4 -3.384 0.0086
## L.B - L.R -0.2109 0.193 17.7 -1.091 0.5318
## S.B - L.R 0.5119 0.221 17.8 2.315 0.0794
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 16.86 | 5.05 | 0.038 |
| 2 | 16.06 | 39.10 | 0.000 |
| 2 | 16.06 | 7.63 | 0.005 |
| <img s | rc="MERDS_R_ | code_SG_reA | nalysis_20200828_files/figure-html/unnamed-chunk-119-1.png" width=“672” /> |
Diagnostic Graphs
rhizosheath_model= lmer(log(RhizosheathSoil_DryRoots_g +1)~precip*soil_root+(1|block), data= SG_roottraits_trt)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(rhizosheath_model))
## [1] 16 2
hist(resid(rhizosheath_model))
shapiro.test(resid(rhizosheath_model))
##
## Shapiro-Wilk normality test
##
## data: resid(rhizosheath_model)
## W = 0.97019, p-value = 0.6068
#0.6068
Raw Statistical output
anova(rhizosheath_model, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.1008 0.10081 1 21 0.1016 0.75304
## soil_root 5.1477 2.57383 2 21 2.5945 0.09841 .
## precip:soil_root 0.1843 0.09213 2 21 0.0929 0.91169
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 21 | 0.10 | 0.753 |
| 2 | 21 | 2.59 | 0.098 |
| 2 | 21 | 0.09 | 0.912 |
Graph for publication
Diagnostic Graphs
SG_roottraits_pres=subset(SG_roottraits_trt, root_association =="B")
rhizosheath_model_pres= lmer(log(RhizosheathSoil_DryRoots_g)~precip*soil_root+(1|block), data= SG_roottraits_pres)
qqPlot(resid(rhizosheath_model_pres))
## 19 24
## 10 15
hist(resid(rhizosheath_model_pres))
shapiro.test(resid(rhizosheath_model_pres))
##
## Shapiro-Wilk normality test
##
## data: resid(rhizosheath_model_pres)
## W = 0.95982, p-value = 0.5982
#0.5982
Raw Statistical output
anova(rhizosheath_model_pres, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.59058 0.59058 1 10.064 1.4693 0.2531
## soil_root 1.72540 1.72540 1 10.064 4.2926 0.0649 .
## precip:soil_root 0.03550 0.03550 1 10.064 0.0883 0.7724
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 10.06 | 1.47 | 0.253 |
| 1 | 10.06 | 4.29 | 0.065 |
| 1 | 10.06 | 0.09 | 0.772 |
| ### Or | igin Rhizosh | eath |
Diagnostic Graphs
SG_roottraits_orig=subset(SG_roottraits_trt,soil_status =="L")
rhizosheath_model_orig= lmer(log(RhizosheathSoil_DryRoots_g+1)~precip*soil_root+(1|block), data= SG_roottraits_orig)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(rhizosheath_model_orig))
## 16 2
## 13 2
hist(resid(rhizosheath_model_orig))
shapiro.test(resid(rhizosheath_model_orig))
##
## Shapiro-Wilk normality test
##
## data: resid(rhizosheath_model_orig)
## W = 0.96907, p-value = 0.7577
#0.7577
Raw Statistical output
anova(rhizosheath_model_orig, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.02583 0.02583 1 15 0.0212 0.8862
## soil_root 1.90925 1.90925 1 15 1.5649 0.2301
## precip:soil_root 0.15779 0.15779 1 15 0.1293 0.7241
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 15 | 0.02 | 0.886 |
| 1 | 15 | 1.56 | 0.230 |
| 1 | 15 | 0.13 | 0.724 |
Diagnostic Graphs
SG_soil_nit_trans_model= lmer((ug_N_NO3_g_dry_soil)~precip*soil_root+(1|block), data= SG_inorg_N_trans_trt)
qqPlot(resid(SG_soil_nit_trans_model))
## 17 15
## 4 2
hist(resid(SG_soil_nit_trans_model))
shapiro.test(resid(SG_soil_nit_trans_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_soil_nit_trans_model)
## W = 0.96397, p-value = 0.4755
Raw Statistical output
anova(SG_soil_nit_trans_model, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 5.3802 5.3802 1 16.868 15.2231 0.001162 **
## soil_root 6.4455 3.2227 2 17.249 9.1186 0.001986 **
## precip:soil_root 3.2720 1.6360 2 16.841 4.6289 0.025001 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_soil_nit_trans_model, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 4.42 0.230 14.5 3.93 4.92
## S.B 3.44 0.201 13.6 3.01 3.87
## L.R 4.52 0.234 16.0 4.03 5.02
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.9848 0.289 17.4 3.413 0.0086
## L.B - L.R -0.0989 0.307 16.8 -0.323 0.9445
## S.B - L.R -1.0837 0.292 16.9 -3.715 0.0047
##
## Results are averaged over the levels of: precip
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates
emmeans(SG_soil_nit_trans_model, pairwise~soil_root|precip)
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 3.86 0.312 19.8 3.21 4.51
## S.B 3.45 0.275 19.6 2.87 4.02
## L.R 3.69 0.275 19.6 3.11 4.26
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 4.99 0.312 19.8 4.34 5.64
## S.B 3.43 0.275 19.6 2.86 4.01
## L.R 5.36 0.365 20.0 4.59 6.12
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.409 0.403 16.8 1.015 0.5780
## L.B - L.R 0.168 0.403 16.8 0.415 0.9099
## S.B - L.R -0.242 0.376 16.1 -0.643 0.7986
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 1.560 0.403 16.8 3.867 0.0034
## L.B - L.R -0.365 0.462 16.8 -0.791 0.7133
## S.B - L.R -1.925 0.446 17.4 -4.315 0.0012
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 16.87 | 15.22 | 0.001 |
| 2 | 17.25 | 9.12 | 0.002 |
| 2 | 16.84 | 4.63 | 0.025 |
| Graph | for publicat | ion | |
| <img s | rc="MERDS_R_ | code_SG_reA | nalysis_20200828_files/figure-html/unnamed-chunk-134-1.png" width=“672” /> |
Diagnostic Graphs
SG_inorg_N_trans_pres=subset(SG_inorg_N_trans_trt, root_association =="B")
SG_soil_nit_trans_model_pres= lmer((ug_N_NO3_g_dry_soil)~precip*soil_root+(1|block), data= SG_inorg_N_trans_pres)
qqPlot(resid(SG_soil_nit_trans_model_pres))
## 17 19
## 1 3
hist(resid(SG_soil_nit_trans_model_pres))
shapiro.test(resid(SG_soil_nit_trans_model_pres))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_soil_nit_trans_model_pres)
## W = 0.89259, p-value = 0.04276
Raw Statistical output
anova(SG_soil_nit_trans_model_pres, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 1.3872 1.3872 1 13.998 5.5927 0.033015 *
## soil_root 4.2187 4.2187 1 13.998 17.0078 0.001033 **
## precip:soil_root 1.4715 1.4715 1 13.998 5.9324 0.028831 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_soil_nit_trans_model_pres, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 4.41 0.183 10.2 4.01 4.82
## S.B 3.44 0.157 10.2 3.09 3.79
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.974 0.242 11.4 4.031 0.0018
##
## Results are averaged over the levels of: precip
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
emmeans(SG_soil_nit_trans_model_pres, pairwise~soil_root|precip)
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 3.85 0.254 14 3.30 4.39
## S.B 3.45 0.223 14 2.97 3.93
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 4.98 0.254 14 4.44 5.53
## S.B 3.43 0.223 14 2.95 3.91
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 0.399 0.338 10.8 1.180 0.2632
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 1.550 0.338 10.8 4.585 0.0008
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 14 | 5.59 | 0.033 |
| 1 | 14 | 17.01 | 0.001 |
| 1 | 14 | 5.93 | 0.029 |
Diagnostic Graphs
SG_inorg_N_trans_orig=subset(SG_inorg_N_trans_trt,soil_status =="L")
SG_soil_nit_trans_model_orig= lmer((ug_N_NO3_g_dry_soil)~precip*soil_root+(1|block), data= SG_inorg_N_trans_orig)
qqPlot(resid(SG_soil_nit_trans_model_orig))
## 17 19
## 4 6
hist(resid(SG_soil_nit_trans_model_orig))
shapiro.test(resid(SG_soil_nit_trans_model_orig))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_soil_nit_trans_model_orig)
## W = 0.96308, p-value = 0.7179
Raw Statistical output
anova(SG_soil_nit_trans_model_orig, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 7.5837 7.5837 1 9.2345 14.0014 0.004408 **
## soil_root 0.0385 0.0385 1 9.2345 0.0711 0.795559
## precip:soil_root 0.2890 0.2890 1 9.2345 0.5335 0.483251
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_soil_nit_trans_model_orig, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 4.43 0.302 7.39 3.72 5.14
## L.R 4.53 0.307 8.59 3.83 5.23
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - L.R -0.1 0.383 8.99 -0.262 0.7992
##
## Results are averaged over the levels of: precip
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
emmeans(SG_soil_nit_trans_model_orig, pairwise~soil_root|precip)
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 3.86 0.399 11.7 2.99 4.74
## L.R 3.69 0.351 11.6 2.92 4.46
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 5.00 0.399 11.7 4.13 5.87
## L.R 5.37 0.473 11.9 4.34 6.40
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - L.R 0.175 0.503 9.05 0.347 0.7362
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - L.R -0.376 0.579 8.95 -0.649 0.5328
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 9.23 | 14.00 | 0.004 |
| 1 | 9.23 | 0.07 | 0.796 |
| 1 | 9.23 | 0.53 | 0.483 |
Diagnostic Graphs
SG_soil_amm_trans_model= lmer(log(ug_N_NH4_g_dry_soil_negto0+0.007)~precip*soil_root+(1|block), data= SG_inorg_N_trans_trt)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(SG_soil_amm_trans_model))
## 20 28
## 7 15
hist(resid(SG_soil_amm_trans_model))
shapiro.test(resid(SG_soil_amm_trans_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_soil_amm_trans_model)
## W = 0.96033, p-value = 0.3981
Raw Statistical output
anova(SG_soil_amm_trans_model, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 7.010 7.0097 1 20 5.3624 0.03131 *
## soil_root 43.257 21.6285 2 20 16.5458 5.755e-05 ***
## precip:soil_root 8.962 4.4812 2 20 3.4281 0.05246 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_soil_amm_trans_model, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B -2.8384 0.415 16.2 -3.718 -1.959
## S.B 0.0188 0.362 16.2 -0.747 0.784
## L.R -2.3990 0.428 17.7 -3.299 -1.499
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log(mu + 0.007) (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B -2.857 0.551 17.5 -5.188 0.0002
## L.B - L.R -0.439 0.588 17.0 -0.747 0.7396
## S.B - L.R 2.418 0.560 17.1 4.317 0.0013
##
## Results are averaged over the levels of: precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
emmeans(SG_soil_amm_trans_model, pairwise~soil_root|precip)
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B -2.56 0.580 20 -3.7734 -1.3554
## S.B -1.10 0.511 20 -2.1707 -0.0376
## L.R -3.13 0.511 20 -4.2015 -2.0683
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B -3.11 0.580 20 -4.3214 -1.9034
## S.B 1.14 0.511 20 0.0751 2.2083
## L.R -1.66 0.686 20 -3.0934 -0.2327
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log(mu + 0.007) (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -1.460 0.773 16.9 -1.889 0.1723
## L.B - L.R 0.571 0.773 16.9 0.738 0.7447
## S.B - L.R 2.031 0.723 16.2 2.808 0.0317
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -4.254 0.773 16.9 -5.504 0.0001
## L.B - L.R -1.449 0.888 17.1 -1.633 0.2593
## S.B - L.R 2.805 0.855 17.7 3.279 0.0112
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 20 | 5.36 | 0.031 |
| 2 | 20 | 16.55 | 0.000 |
| 2 | 20 | 3.43 | 0.052 |
Graph for publication
Diagnostic Graphs
SG_inorg_N_trans_pres=subset(SG_inorg_N_trans_trt, root_association =="B")
SG_soil_amm_trans_model_pres= lmer(sqrt(ug_N_NH4_g_dry_soil_negto0)~precip*soil_root+(1|block), data= SG_inorg_N_trans_pres)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(SG_soil_amm_trans_model_pres))
## 24 22
## 8 6
hist(resid(SG_soil_amm_trans_model_pres))
shapiro.test(resid(SG_soil_amm_trans_model_pres))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_soil_amm_trans_model_pres)
## W = 0.93074, p-value = 0.2001
Raw Statistical output
anova(SG_soil_amm_trans_model_pres, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 1.3408 1.3408 1 14 18.813 0.0006824 ***
## soil_root 3.8066 3.8066 1 14 53.410 3.86e-06 ***
## precip:soil_root 1.7746 1.7746 1 14 24.899 0.0001982 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_soil_amm_trans_model_pres, pairwise~soil_root|precip)
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.317 0.136 14 0.0245 0.609
## S.B 0.610 0.119 14 0.3543 0.866
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.234 0.136 14 -0.0581 0.526
## S.B 1.792 0.119 14 1.5354 2.048
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the sqrt (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -0.294 0.181 10.8 -1.620 0.1338
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B -1.557 0.181 10.8 -8.596 <.0001
##
## Note: contrasts are still on the sqrt scale
## Degrees-of-freedom method: kenward-roger
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 14 | 18.81 | 0.001 |
| 1 | 14 | 53.41 | 0.000 |
| 1 | 14 | 24.90 | 0.000 |
Diagnostic Graphs
SG_inorg_N_trans_orig=subset(SG_inorg_N_trans_trt,soil_status =="L")
SG_soil_amm_trans_model_orig= lmer((ug_N_NH4_g_dry_soil_negto0)~precip*soil_root+(1|block), data= SG_inorg_N_trans_orig)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(SG_soil_amm_trans_model_orig))
## 31 16
## 13 3
hist(resid(SG_soil_amm_trans_model_orig))
shapiro.test(resid(SG_soil_amm_trans_model_orig))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_soil_amm_trans_model_orig)
## W = 0.9063, p-value = 0.1014
Raw Statistical output
anova(SG_soil_amm_trans_model_orig, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 0.006632 0.006632 1 12 0.4456 0.5171
## soil_root 0.001692 0.001692 1 12 0.1137 0.7418
## precip:soil_root 0.033168 0.033168 1 12 2.2285 0.1613
emmeans(SG_soil_amm_trans_model_orig, pairwise~soil_root|precip)
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.1422 0.0618 12 0.00754 0.277
## L.R 0.0705 0.0546 12 -0.04833 0.189
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 0.0910 0.0618 12 -0.04363 0.226
## L.R 0.2045 0.0745 12 0.04209 0.367
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - L.R 0.0717 0.0824 9.12 0.869 0.4070
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - L.R -0.1135 0.0958 9.27 -1.184 0.2657
##
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 12 | 0.45 | 0.517 |
| 1 | 12 | 0.11 | 0.742 |
| 1 | 12 | 2.23 | 0.161 |
Diagnostic Graphs
SG_soil_VWC_model= lmer((percent_soil_moisture_dry_weight)~precip*soil_root*life_stage+(1|block), data= SG_inorg_N_trt)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(SG_soil_VWC_model))
## [1] 20 33
hist(resid(SG_soil_VWC_model))
shapiro.test(resid(SG_soil_VWC_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_soil_VWC_model)
## W = 0.96851, p-value = 0.3377
#0.3377
Raw Statistical output
anova(SG_soil_VWC_model, type=3)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## precip 307.117 307.117 1 27 7.9808 0.008782 **
## soil_root 41.285 20.643 2 27 0.5364 0.590938
## life_stage 135.010 135.010 1 27 3.5084 0.071923 .
## precip:soil_root 22.074 11.037 2 27 0.2868 0.752914
## precip:life_stage 0.405 0.405 1 27 0.0105 0.919080
## soil_root:life_stage 13.084 6.542 2 27 0.1700 0.844555
## precip:soil_root:life_stage 3.642 1.821 2 27 0.0473 0.953857
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_soil_VWC_model, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B 11.96 2.17 21.0 7.45 16.5
## S.B 8.86 2.20 23.1 4.32 13.4
## L.R 10.60 1.80 16.9 6.81 14.4
##
## Results are averaged over the levels of: precip, life_stage
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B 3.10 3.06 25.0 1.011 0.5771
## L.B - L.R 1.35 2.74 23.6 0.493 0.8753
## S.B - L.R -1.74 2.82 24.7 -0.618 0.8117
##
## Results are averaged over the levels of: precip, life_stage
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates
emmeans(SG_soil_VWC_model, pairwise~soil_root|precip)
## NOTE: Results may be misleading due to involvement in interactions
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip = A:
## soil_root emmean SE df lower.CL upper.CL
## L.B 15.40 2.43 24.2 10.396 20.4
## S.B 11.00 2.68 25.7 5.489 16.5
## L.R 14.83 2.09 24.1 10.524 19.1
##
## precip = D:
## soil_root emmean SE df lower.CL upper.CL
## L.B 8.51 3.68 26.4 0.958 16.1
## S.B 6.73 3.59 26.5 -0.639 14.1
## L.R 6.37 2.90 26.4 0.408 12.3
##
## Results are averaged over the levels of: life_stage
## Degrees-of-freedom method: kenward-roger
## Results are given on the ( (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## precip = A:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 4.408 3.63 25.7 1.213 0.4564
## L.B - L.R 0.570 3.18 24.2 0.179 0.9825
## S.B - L.R -3.838 3.39 24.7 -1.133 0.5033
##
## precip = D:
## contrast estimate SE df t.ratio p.value
## L.B - S.B 1.784 5.20 26.9 0.343 0.9373
## L.B - L.R 2.136 4.53 24.1 0.472 0.8852
## S.B - L.R 0.352 4.66 26.5 0.075 0.9969
##
## Results are averaged over the levels of: life_stage
## Note: contrasts are still on the ( scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
| Df | Resid.Df | F.value | P.value |
|---|---|---|---|
| 1 | 27 | 7.98 | 0.009 |
| 2 | 27 | 0.54 | 0.591 |
| 1 | 27 | 3.51 | 0.072 |
| 2 | 27 | 0.29 | 0.753 |
| 1 | 27 | 0.01 | 0.919 |
| 2 | 27 | 0.17 | 0.845 |
| 2 | 27 | 0.05 | 0.954 |
Diagnostic Graphs
SG_start_inorg_N$soil_root=with(SG_start_inorg_N, interaction(soil_status,root_association))
SG_Soil_nit_start= lm((ug_N_NO3_g_dry_soil)~soil_root+block, data= SG_start_inorg_N)
qqPlot(resid(SG_Soil_nit_start))
## [1] 14 7
hist(resid(SG_Soil_nit_start))
shapiro.test(resid(SG_Soil_nit_start))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_Soil_nit_start)
## W = 0.94653, p-value = 0.4716
Raw Statistical output
Anova(SG_Soil_nit_start,type = 3)
## Anova Table (Type III tests)
##
## Response: (ug_N_NO3_g_dry_soil)
## Sum Sq Df F value Pr(>F)
## (Intercept) 124.752 1 49.7581 2.116e-05 ***
## soil_root 3.977 2 0.7931 0.4767
## block 3.893 1 1.5529 0.2386
## Residuals 27.579 11
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Formatted Anova table
| Df | F.value | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 49.76 | 0.000 |
| soil_root | 2 | 0.79 | 0.477 |
| block | 1 | 1.55 | 0.239 |
| Residuals | 11 | NA | NA |
Graph for publication
Diagnostic Graphs
SG_start_inorg_N_pres=subset(SG_start_inorg_N, root_association =="B")
SG_Soil_nit_start_pres= lm((ug_N_NO3_g_dry_soil)~soil_root+block, data= SG_start_inorg_N_pres)
qqPlot(resid(SG_Soil_nit_start_pres))
## 14 1
## 9 1
hist(resid(SG_Soil_nit_start_pres))
shapiro.test(resid(SG_Soil_nit_start_pres))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_Soil_nit_start_pres)
## W = 0.93286, p-value = 0.4766
Raw Statistical output
Anova(SG_Soil_nit_start_pres,type = 3)
## Anova Table (Type III tests)
##
## Response: (ug_N_NO3_g_dry_soil)
## Sum Sq Df F value Pr(>F)
## (Intercept) 75.236 1 32.3655 0.0007437 ***
## soil_root 2.846 1 1.2242 0.3051005
## block 5.728 1 2.4643 0.1604494
## Residuals 16.272 7
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Formatted Anova table
| Df | F.value | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 32.37 | 0.001 |
| soil_root | 1 | 1.22 | 0.305 |
| block | 1 | 2.46 | 0.160 |
| Residuals | 7 | NA | NA |
Diagnostic Graphs
SG_start_inorg_N_orig=subset(SG_start_inorg_N, soil_status =="L")
SG_Soil_nit_start_orig= lm((ug_N_NO3_g_dry_soil)^3~soil_root+block, data= SG_start_inorg_N_orig)
qqPlot(resid(SG_Soil_nit_start_orig))
## [1] 3 7
hist(resid(SG_Soil_nit_start_orig))
shapiro.test(resid(SG_Soil_nit_start_orig))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_Soil_nit_start_orig)
## W = 0.82833, p-value = 0.03194
boxCox(SG_Soil_nit_start_orig)
Raw Statistical output
Anova(SG_Soil_nit_start_orig,type = 3)
## Anova Table (Type III tests)
##
## Response: (ug_N_NO3_g_dry_soil)^3
## Sum Sq Df F value Pr(>F)
## (Intercept) 496747 1 7.4104 0.02967 *
## soil_root 104794 1 1.5633 0.25136
## block 2696 1 0.0402 0.84675
## Residuals 469239 7
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Formatted Anova table
| Df | F.value | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 7.41 | 0.030 |
| soil_root | 1 | 1.56 | 0.251 |
| block | 1 | 0.04 | 0.847 |
| Residuals | 7 | NA | NA |
Diagnostic Graphs
SG_start_inorg_N$soil_root=with(SG_start_inorg_N, interaction(soil_status,root_association))
SG_Soil_amm_start= lm(log(ug_N_NH4_g_dry_soil)~soil_root+block, data= SG_start_inorg_N)
qqPlot(resid(SG_Soil_amm_start))
## [1] 4 10
hist(resid(SG_Soil_amm_start))
shapiro.test(resid(SG_Soil_amm_start))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_Soil_amm_start)
## W = 0.93105, p-value = 0.2829
boxCox(SG_Soil_amm_start)
Raw Statistical output
Anova(SG_Soil_amm_start,type = 3)
## Anova Table (Type III tests)
##
## Response: log(ug_N_NH4_g_dry_soil)
## Sum Sq Df F value Pr(>F)
## (Intercept) 9.9251 1 98.8744 7.823e-07 ***
## soil_root 12.6065 2 62.7930 9.615e-07 ***
## block 0.0374 1 0.3728 0.5539
## Residuals 1.1042 11
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Formatted Anova table
| Df | F.value | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 98.87 | 0.000 |
| soil_root | 2 | 62.79 | 0.000 |
| block | 1 | 0.37 | 0.554 |
| Residuals | 11 | NA | NA |
Graph for publication
Diagnostic Graphs
SG_start_inorg_N_pres=subset(SG_start_inorg_N, root_association =="B")
SG_Soil_amm_start_pres= lm((ug_N_NH4_g_dry_soil)~soil_root+block, data= SG_start_inorg_N_pres)
qqPlot(resid(SG_Soil_amm_start_pres))
## 14 15
## 9 10
hist(resid(SG_Soil_amm_start_pres))
shapiro.test(resid(SG_Soil_amm_start_pres))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_Soil_amm_start_pres)
## W = 0.87313, p-value = 0.1087
boxCox(SG_Soil_amm_start_pres)
Raw Statistical output
Anova(SG_Soil_amm_start_pres,type = 3)
## Anova Table (Type III tests)
##
## Response: (ug_N_NH4_g_dry_soil)
## Sum Sq Df F value Pr(>F)
## (Intercept) 247.50 1 9.3004 0.0185923 *
## soil_root 1423.78 1 53.5011 0.0001608 ***
## block 44.24 1 1.6626 0.2382233
## Residuals 186.29 7
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Formatted Anova table
| Df | F.value | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 9.30 | 0.019 |
| soil_root | 1 | 53.50 | 0.000 |
| block | 1 | 1.66 | 0.238 |
| Residuals | 7 | NA | NA |
Diagnostic Graphs
SG_start_inorg_N_orig=subset(SG_start_inorg_N, soil_status =="L")
SG_Soil_amm_start_orig= lm((ug_N_NH4_g_dry_soil)^-1~soil_root+block, data= SG_start_inorg_N_orig)
qqPlot(resid(SG_Soil_amm_start_orig))
## [1] 4 10
hist(resid(SG_Soil_amm_start_orig))
shapiro.test(resid(SG_Soil_amm_start_orig))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_Soil_amm_start_orig)
## W = 0.96944, p-value = 0.8856
boxCox(SG_Soil_amm_start_orig)
Raw Statistical output
Anova(SG_Soil_amm_start_orig,type = 3)
## Anova Table (Type III tests)
##
## Response: (ug_N_NH4_g_dry_soil)^-1
## Sum Sq Df F value Pr(>F)
## (Intercept) 0.128490 1 18.228 0.003704 **
## soil_root 0.000268 1 0.038 0.850978
## block 0.000000 1 0.000 0.996817
## Residuals 0.049344 7
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Formatted Anova table
| Df | F.value | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 18.23 | 0.004 |
| soil_root | 1 | 0.04 | 0.851 |
| block | 1 | 0.00 | 0.997 |
| Residuals | 7 | NA | NA |
Diagnostic Graphs
SG_Soil_DOC_mod= lm(log(unfumigated_DOC_concentration_ugC_gsoil)~soil_root+block, data= SG_MBC_DOC_trt)
qqPlot(resid(SG_Soil_DOC_mod))
## [1] 6 2
hist(resid(SG_Soil_DOC_mod))
shapiro.test(resid(SG_Soil_DOC_mod))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_Soil_DOC_mod)
## W = 0.9533, p-value = 0.6131
boxCox(SG_Soil_DOC_mod)
Raw Statistical output
Anova(SG_Soil_DOC_mod,type = 3)
## Anova Table (Type III tests)
##
## Response: log(unfumigated_DOC_concentration_ugC_gsoil)
## Sum Sq Df F value Pr(>F)
## (Intercept) 16.5452 1 38.7139 9.857e-05 ***
## soil_root 2.2287 2 2.6074 0.1226
## block 0.0006 1 0.0014 0.9712
## Residuals 4.2737 10
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Formatted Anova table
| Df | F.value | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 38.71 | 0.000 |
| soil_root | 2 | 2.61 | 0.123 |
| block | 1 | 0.00 | 0.971 |
| Residuals | 10 | NA | NA |
Graph for publication
Diagnostic Graphs
#data_SG_biomass_trans_surv_drought=subset(data_SG_biomass_trans_surv_trt, precip=="D")
SG_combin_surv_model= glmer(surv~soil_root*precip*life_stage+(1|block/life_stage), data= data_SG_biomass_surv_trt_comb, family = binomial)
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## unable to evaluate scaled gradient
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge: degenerate Hessian with 3 negative eigenvalues
qqPlot(resid(SG_combin_surv_model))
## 24 29
## 14 88
hist(resid(SG_combin_surv_model))
shapiro.test(resid(SG_combin_surv_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_combin_surv_model)
## W = 0.83916, p-value = 1.729e-11
Raw Statistical output
Anova(SG_combin_surv_model,type = 3)
## Warning in vcov.merMod(mod, complete = FALSE): variance-covariance matrix computed from finite-difference Hessian is
## not positive definite or contains NA values: falling back to var-cov estimated from RX
## Warning in vcov.merMod(mod, complete = FALSE): variance-covariance matrix computed from finite-difference Hessian is
## not positive definite or contains NA values: falling back to var-cov estimated from RX
## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: surv
## Chisq Df Pr(>Chisq)
## (Intercept) 0 1 0.9949
## soil_root 0 2 1.0000
## precip 0 1 0.9960
## life_stage 0 1 0.9959
## soil_root:precip 0 2 1.0000
## soil_root:life_stage 0 2 1.0000
## precip:life_stage 0 1 0.9961
## soil_root:precip:life_stage 0 2 1.0000
emmeans(SG_combin_surv_model, pairwise~soil_root)
## Warning in vcov.merMod(object, correlation = FALSE): variance-covariance matrix computed from finite-difference Hessian is
## not positive definite or contains NA values: falling back to var-cov estimated from RX
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 6.67 1656 Inf -3239 3253
## S.B 5.37 1762 Inf -3449 3460
## L.R 6.44 1555 Inf -3042 3055
##
## Results are averaged over the levels of: precip, life_stage
## Results are given on the logit (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df z.ratio p.value
## L.B - S.B 1.297 2418 Inf 0.001 1.0000
## L.B - L.R 0.225 2272 Inf 0.000 1.0000
## S.B - L.R -1.071 2351 Inf 0.000 1.0000
##
## Results are averaged over the levels of: precip, life_stage
## Results are given on the log odds ratio (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
## Warning in vcov.merMod(mod, complete = FALSE): variance-covariance matrix computed from finite-difference Hessian is
## not positive definite or contains NA values: falling back to var-cov estimated from RX
## Warning in vcov.merMod(mod, complete = FALSE): variance-covariance matrix computed from finite-difference Hessian is
## not positive definite or contains NA values: falling back to var-cov estimated from RX
| Df | Chi.Sq | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 0 | 0.995 |
| soil_root | 2 | 0 | 1.000 |
| precip | 1 | 0 | 0.996 |
| life_stage | 1 | 0 | 0.996 |
| soil_root:precip | 2 | 0 | 1.000 |
| soil_root:life_stage | 2 | 0 | 1.000 |
| precip:life_stage | 1 | 0 | 0.996 |
| soil_root:precip:life_stage | 2 | 0 | 1.000 |
Diagnostic Graphs
data_SG_biomass_surv_trt_comb_drought=subset(data_SG_biomass_surv_trt_comb, precip=="D")
SG_combin_surv_drought_model= glmer(surv~soil_root*life_stage+(1|block/life_stage), data= data_SG_biomass_surv_trt_comb_drought, family = binomial)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(SG_combin_surv_drought_model))
## 24 29
## 14 53
hist(resid(SG_combin_surv_drought_model))
shapiro.test(resid(SG_combin_surv_drought_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_combin_surv_drought_model)
## W = 0.76715, p-value = 4.209e-09
Raw Statistical output
Anova(SG_combin_surv_drought_model,type = 3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: surv
## Chisq Df Pr(>Chisq)
## (Intercept) 6.5558 1 0.01045 *
## soil_root 6.1744 2 0.04563 *
## life_stage 0.1295 1 0.71900
## soil_root:life_stage 3.7279 2 0.15506
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_combin_surv_drought_model, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 2.1866 0.778 Inf 0.662 3.71
## S.B 0.0958 0.668 Inf -1.214 1.41
## L.R 1.7439 0.761 Inf 0.253 3.23
##
## Results are averaged over the levels of: life_stage
## Results are given on the logit (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df z.ratio p.value
## L.B - S.B 2.091 0.896 Inf 2.335 0.0511
## L.B - L.R 0.443 0.912 Inf 0.486 0.8781
## S.B - L.R -1.648 0.886 Inf -1.860 0.1504
##
## Results are averaged over the levels of: life_stage
## Results are given on the log odds ratio (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
Formatted Anova table
| Df | Chi.Sq | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 6.56 | 0.010 |
| soil_root | 2 | 6.17 | 0.046 |
| life_stage | 1 | 0.13 | 0.719 |
| soil_root:life_stage | 2 | 3.73 | 0.155 |
| ### Presence combined s | urviva | l | |
| Diagnostic Graphs |
data_SG_biomass_surv_trt_comb_drought_pres=subset(data_SG_biomass_surv_trt_comb_drought, root_association =="B")
SG_combin_surv_drought_pres_model= glmer(surv~soil_root*life_stage+(1|block/life_stage), data= data_SG_biomass_surv_trt_comb_drought_pres, family = binomial)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(SG_combin_surv_drought_pres_model))
## 24 16
## 6 17
hist(resid(SG_combin_surv_drought_pres_model))
shapiro.test(resid(SG_combin_surv_drought_pres_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_combin_surv_drought_pres_model)
## W = 0.74597, p-value = 1.487e-07
Raw Statistical output
Anova(SG_combin_surv_drought_pres_model,type = 3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: surv
## Chisq Df Pr(>Chisq)
## (Intercept) 6.9271 1 0.00849 **
## soil_root 5.0619 1 0.02446 *
## life_stage 0.6846 1 0.40800
## soil_root:life_stage 1.4832 1 0.22328
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_combin_surv_drought_pres_model, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 2.035 0.650 Inf 0.761 3.31
## S.B 0.159 0.522 Inf -0.864 1.18
##
## Results are averaged over the levels of: life_stage
## Results are given on the logit (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df z.ratio p.value
## L.B - S.B 1.88 0.834 Inf 2.250 0.0245
##
## Results are averaged over the levels of: life_stage
## Results are given on the log odds ratio (not the response) scale.
Formatted Anova table
| Df | Chi.Sq | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 6.93 | 0.008 |
| soil_root | 1 | 5.06 | 0.024 |
| life_stage | 1 | 0.68 | 0.408 |
| soil_root:life_stage | 1 | 1.48 | 0.223 |
Diagnostic Graphs
data_SG_biomass_surv_trt_comb_drought_orig=subset(data_SG_biomass_surv_trt_comb_drought, soil_status =="L")
SG_combin_surv_drought_orig_model= glmer(surv~soil_root*life_stage+(1|block/life_stage), data= data_SG_biomass_surv_trt_comb_drought_orig, family = binomial)
qqPlot(resid(SG_combin_surv_drought_orig_model))
## 29 24
## 47 14
hist(resid(SG_combin_surv_drought_orig_model))
shapiro.test(resid(SG_combin_surv_drought_orig_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_combin_surv_drought_orig_model)
## W = 0.61185, p-value = 4.955e-10
Raw Statistical output
Anova(SG_combin_surv_drought_orig_model,type = 3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: surv
## Chisq Df Pr(>Chisq)
## (Intercept) 10.0712 1 0.001506 **
## soil_root 0.4678 1 0.493979
## life_stage 0.3427 1 0.558290
## soil_root:life_stage 0.0938 1 0.759389
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_combin_surv_drought_orig_model, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df asymp.LCL asymp.UCL
## L.B 2.23 0.813 Inf 0.637 3.82
## L.R 1.58 0.712 Inf 0.188 2.98
##
## Results are averaged over the levels of: life_stage
## Results are given on the logit (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df z.ratio p.value
## L.B - L.R 0.646 0.944 Inf 0.684 0.4940
##
## Results are averaged over the levels of: life_stage
## Results are given on the log odds ratio (not the response) scale.
Formatted Anova table
| Df | Chi.Sq | P.value | |
|---|---|---|---|
| (Intercept) | 1 | 10.07 | 0.002 |
| soil_root | 1 | 0.47 | 0.494 |
| life_stage | 1 | 0.34 | 0.558 |
| soil_root:life_stage | 1 | 0.09 | 0.759 |
Diagnostic Graphs
SG_combin_biomass_model= lmer(log(total_biomass+0.001)~soil_root*precip*life_stage+(1|block/life_stage), data= data_SG_biomass_trt_comb)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(SG_combin_biomass_model))
## 29 41
## 74 86
hist(resid(SG_combin_biomass_model))
shapiro.test(resid(SG_combin_biomass_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_combin_biomass_model)
## W = 0.97333, p-value = 0.009383
Raw Statistical output
anova(SG_combin_biomass_model)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## soil_root 16.1994 8.0997 2 120.64 4.2800 0.016003 *
## precip 4.8969 4.8969 1 119.83 2.5876 0.110338
## life_stage 8.0818 8.0818 1 122.02 4.2705 0.040894 *
## soil_root:precip 3.1145 1.5573 2 121.19 0.8229 0.441607
## soil_root:life_stage 1.5159 0.7580 2 120.64 0.4005 0.670864
## precip:life_stage 12.5200 12.5200 1 119.83 6.6157 0.011330 *
## soil_root:precip:life_stage 26.2502 13.1251 2 121.19 6.9355 0.001407 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_combin_biomass_model, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B -3.21 0.244 12.6 -3.74 -2.68
## S.B -2.21 0.357 39.6 -2.93 -1.49
## L.R -3.24 0.250 13.3 -3.78 -2.70
##
## Results are averaged over the levels of: precip, life_stage
## Degrees-of-freedom method: kenward-roger
## Results are given on the log(mu + 0.001) (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B -1.0068 0.383 121 -2.627 0.0261
## L.B - L.R 0.0259 0.291 118 0.089 0.9956
## S.B - L.R 1.0327 0.394 120 2.622 0.0265
##
## Results are averaged over the levels of: precip, life_stage
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 3 estimates
emmeans(SG_combin_biomass_model, pairwise~life_stage)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## life_stage emmean SE df lower.CL upper.CL
## germinant -2.59 0.292 16.74 -3.21 -1.97
## seedling -3.18 0.198 4.93 -3.69 -2.67
##
## Results are averaged over the levels of: soil_root, precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log(mu + 0.001) (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## germinant - seedling 0.593 0.297 5.87 1.996 0.0940
##
## Results are averaged over the levels of: soil_root, precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
emmeans(SG_combin_biomass_model, pairwise~precip*life_stage)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## precip life_stage emmean SE df lower.CL upper.CL
## A germinant -2.73 0.322 26.6 -3.39 -2.07
## D germinant -2.45 0.437 57.6 -3.33 -1.58
## A seedling -2.59 0.245 11.6 -3.12 -2.05
## D seedling -3.78 0.245 11.6 -4.31 -3.24
##
## Results are averaged over the levels of: soil_root
## Degrees-of-freedom method: kenward-roger
## Results are given on the log(mu + 0.001) (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## A,germinant - D,germinant -0.275 0.497 119.8 -0.552 0.9458
## A,germinant - A,seedling -0.140 0.357 13.4 -0.391 0.9789
## A,germinant - D,seedling 1.052 0.357 13.4 2.943 0.0482
## D,germinant - A,seedling 0.135 0.463 28.7 0.291 0.9912
## D,germinant - D,seedling 1.327 0.463 28.7 2.862 0.0369
## A,seedling - D,seedling 1.192 0.290 115.7 4.109 0.0004
##
## Results are averaged over the levels of: soil_root
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 4 estimates
emmeans(SG_combin_biomass_model, pairwise~life_stage|soil_root|precip)
## $emmeans
## soil_root = L.B, precip = A:
## life_stage emmean SE df lower.CL upper.CL
## germinant -2.657 0.464 74.8 -3.58 -1.733
## seedling -3.161 0.380 52.7 -3.92 -2.399
##
## soil_root = S.B, precip = A:
## life_stage emmean SE df lower.CL upper.CL
## germinant -3.218 0.642 109.2 -4.49 -1.947
## seedling -1.298 0.380 52.7 -2.06 -0.536
##
## soil_root = L.R, precip = A:
## life_stage emmean SE df lower.CL upper.CL
## germinant -2.304 0.424 64.2 -3.15 -1.457
## seedling -3.301 0.380 52.7 -4.06 -2.540
##
## soil_root = L.B, precip = D:
## life_stage emmean SE df lower.CL upper.CL
## germinant -3.412 0.485 82.6 -4.38 -2.448
## seedling -3.621 0.380 52.7 -4.38 -2.859
##
## soil_root = S.B, precip = D:
## life_stage emmean SE df lower.CL upper.CL
## germinant -0.642 1.058 102.9 -2.74 1.456
## seedling -3.666 0.380 52.7 -4.43 -2.904
##
## soil_root = L.R, precip = D:
## life_stage emmean SE df lower.CL upper.CL
## germinant -3.301 0.556 90.3 -4.41 -2.197
## seedling -4.048 0.380 52.7 -4.81 -3.287
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log(mu + 0.001) (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## soil_root = L.B, precip = A:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 0.504 0.568 59.1 0.887 0.3786
##
## soil_root = S.B, precip = A:
## contrast estimate SE df t.ratio p.value
## germinant - seedling -1.920 0.721 86.3 -2.663 0.0092
##
## soil_root = L.R, precip = A:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 0.997 0.537 53.4 1.858 0.0687
##
## soil_root = L.B, precip = D:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 0.209 0.586 64.1 0.356 0.7229
##
## soil_root = S.B, precip = D:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 3.024 1.108 89.6 2.729 0.0076
##
## soil_root = L.R, precip = D:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 0.747 0.646 68.9 1.157 0.2513
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
Formatted Anova table
| Df | Resid.Df | F.value | P.value | |
|---|---|---|---|---|
| soil_root | 2 | 120.63 | 4.28 | 0.016 |
| precip | 1 | 119.83 | 2.59 | 0.110 |
| life_stage | 1 | 122.02 | 4.27 | 0.041 |
| soil_root:precip | 2 | 121.20 | 0.82 | 0.442 |
| soil_root:life_stage | 2 | 120.63 | 0.40 | 0.671 |
| precip:life_stage | 1 | 119.83 | 6.62 | 0.011 |
| soil_root:precip:life_stage | 2 | 121.20 | 6.94 | 0.001 |
| ### Presence Combined Biomass |
Diagnostic Graphs
data_SG_biomass_trt_comb_pres=subset(data_SG_biomass_trt_comb, root_association =="B")
SG_combin_biomass_pres_model= lmer(log(total_biomass+0.001)~soil_root*precip*life_stage+(1|block/life_stage), data= data_SG_biomass_trt_comb_pres)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(SG_combin_biomass_pres_model))
## 41 36
## 52 47
hist(resid(SG_combin_biomass_pres_model))
shapiro.test(resid(SG_combin_biomass_pres_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_combin_biomass_pres_model)
## W = 0.95636, p-value = 0.005474
Raw Statistical output
anova(SG_combin_biomass_pres_model)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## soil_root 14.6111 14.6111 1 76.129 7.7962 0.0066170 **
## precip 0.6526 0.6526 1 76.407 0.3482 0.5568529
## life_stage 3.1065 3.1065 1 77.802 1.6576 0.2017495
## soil_root:precip 2.0195 2.0195 1 77.573 1.0776 0.3024683
## soil_root:life_stage 0.2408 0.2408 1 76.129 0.1285 0.7209959
## precip:life_stage 19.0950 19.0950 1 76.407 10.1887 0.0020518 **
## soil_root:precip:life_stage 24.0017 24.0017 1 77.573 12.8068 0.0005993 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_combin_biomass_pres_model, pairwise~soil_root)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## soil_root emmean SE df lower.CL upper.CL
## L.B -3.22 0.235 8.46 -3.75 -2.68
## S.B -2.17 0.357 27.22 -2.91 -1.44
##
## Results are averaged over the levels of: precip, life_stage
## Degrees-of-freedom method: kenward-roger
## Results are given on the log(mu + 0.001) (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## L.B - S.B -1.04 0.387 76.3 -2.694 0.0087
##
## Results are averaged over the levels of: precip, life_stage
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
emmeans(SG_combin_biomass_pres_model, pairwise~precip*life_stage)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## precip life_stage emmean SE df lower.CL upper.CL
## A germinant -2.94 0.403 37.1 -3.76 -2.122
## D germinant -1.97 0.606 47.9 -3.18 -0.748
## A seedling -2.23 0.275 13.5 -2.82 -1.637
## D seedling -3.64 0.275 13.5 -4.24 -3.051
##
## Results are averaged over the levels of: soil_root
## Degrees-of-freedom method: kenward-roger
## Results are given on the log(mu + 0.001) (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## A,germinant - D,germinant -0.973 0.694 76.7 -1.402 0.5021
## A,germinant - A,seedling -0.709 0.460 14.4 -1.542 0.4399
## A,germinant - D,seedling 0.705 0.460 14.4 1.531 0.4454
## D,germinant - A,seedling 0.263 0.645 24.7 0.408 0.9765
## D,germinant - D,seedling 1.677 0.645 24.7 2.601 0.0689
## A,seedling - D,seedling 1.414 0.353 71.1 4.000 0.0009
##
## Results are averaged over the levels of: soil_root
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 4 estimates
emmeans(SG_combin_biomass_pres_model, pairwise~life_stage|soil_root|precip)
## $emmeans
## soil_root = L.B, precip = A:
## life_stage emmean SE df lower.CL upper.CL
## germinant -2.661 0.461 49.7 -3.59 -1.734
## seedling -3.161 0.372 36.6 -3.92 -2.407
##
## soil_root = S.B, precip = A:
## life_stage emmean SE df lower.CL upper.CL
## germinant -3.217 0.642 70.8 -4.50 -1.938
## seedling -1.298 0.372 36.6 -2.05 -0.544
##
## soil_root = L.B, precip = D:
## life_stage emmean SE df lower.CL upper.CL
## germinant -3.422 0.482 55.1 -4.39 -2.456
## seedling -3.621 0.372 36.6 -4.37 -2.867
##
## soil_root = S.B, precip = D:
## life_stage emmean SE df lower.CL upper.CL
## germinant -0.511 1.094 62.9 -2.70 1.675
## seedling -3.666 0.372 36.6 -4.42 -2.912
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log(mu + 0.001) (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## soil_root = L.B, precip = A:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 0.501 0.570 28.5 0.879 0.3867
##
## soil_root = S.B, precip = A:
## contrast estimate SE df t.ratio p.value
## germinant - seedling -1.919 0.723 46.7 -2.653 0.0109
##
## soil_root = L.B, precip = D:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 0.200 0.586 31.5 0.341 0.7357
##
## soil_root = S.B, precip = D:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 3.155 1.144 52.0 2.759 0.0080
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
Formatted Anova table
| Df | Resid.Df | F.value | P.value | |
|---|---|---|---|---|
| soil_root | 1 | 76.13 | 7.80 | 0.007 |
| precip | 1 | 76.41 | 0.35 | 0.557 |
| life_stage | 1 | 77.80 | 1.66 | 0.202 |
| soil_root:precip | 1 | 77.57 | 1.08 | 0.302 |
| soil_root:life_stage | 1 | 76.13 | 0.13 | 0.721 |
| precip:life_stage | 1 | 76.41 | 10.19 | 0.002 |
| soil_root:precip:life_stage | 1 | 77.57 | 12.81 | 0.001 |
Diagnostic Graphs
data_SG_biomass_trt_comb_orig=subset(data_SG_biomass_trt_comb, soil_status =="L")
SG_combin_biomass_orig_model= lmer(log(total_biomass+0.001)~soil_root*precip*life_stage+(1|block/life_stage), data= data_SG_biomass_trt_comb_orig)
qqPlot(resid(SG_combin_biomass_orig_model))
## 29 16
## 67 54
hist(resid(SG_combin_biomass_orig_model))
shapiro.test(resid(SG_combin_biomass_orig_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_combin_biomass_orig_model)
## W = 0.98373, p-value = 0.2687
Raw Statistical output
anova(SG_combin_biomass_orig_model)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## soil_root 0.0170 0.0170 1 85.439 0.0100 0.920743
## precip 12.2652 12.2652 1 87.205 7.1861 0.008784 **
## life_stage 6.5403 6.5403 1 4.368 3.8319 0.115906
## soil_root:precip 0.4565 0.4565 1 84.367 0.2674 0.606410
## soil_root:life_stage 1.4816 1.4816 1 85.439 0.8681 0.354118
## precip:life_stage 0.4221 0.4221 1 87.205 0.2473 0.620225
## soil_root:precip:life_stage 0.0001 0.0001 1 84.367 0.0000 0.995601
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_combin_biomass_orig_model, pairwise~precip)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## precip emmean SE df lower.CL upper.CL
## A -2.85 0.224 8.49 -3.36 -2.34
## D -3.59 0.243 11.13 -4.12 -3.05
##
## Results are averaged over the levels of: soil_root, life_stage
## Degrees-of-freedom method: kenward-roger
## Results are given on the log(mu + 0.001) (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## A - D 0.741 0.281 86.7 2.636 0.0099
##
## Results are averaged over the levels of: soil_root, life_stage
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
Formatted Anova table
| Df | Resid.Df | F.value | P.value | |
|---|---|---|---|---|
| soil_root | 1 | 85.44 | 0.01 | 0.921 |
| precip | 1 | 87.20 | 7.19 | 0.009 |
| life_stage | 1 | 4.37 | 3.83 | 0.116 |
| soil_root:precip | 1 | 84.37 | 0.27 | 0.606 |
| soil_root:life_stage | 1 | 85.44 | 0.87 | 0.354 |
| precip:life_stage | 1 | 87.20 | 0.25 | 0.620 |
| soil_root:precip:life_stage | 1 | 84.37 | 0.00 | 0.996 |
Diagnostic Graphs
SG_combin_root_shoot_model= lmer(log(root_shoot+0.001)~soil_root*precip*life_stage+(1|block/life_stage), data= data_SG_root_shoot_trt_comb)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(SG_combin_root_shoot_model))
## 531 45
## 88 80
hist(resid(SG_combin_root_shoot_model))
shapiro.test(resid(SG_combin_root_shoot_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_combin_root_shoot_model)
## W = 0.97959, p-value = 0.05557
Raw Statistical output
anova(SG_combin_root_shoot_model)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## soil_root 1.231 0.615 2 113 0.4566 0.63462
## precip 8.680 8.680 1 113 6.4396 0.01252 *
## life_stage 31.625 31.625 1 113 23.4632 4.08e-06 ***
## soil_root:precip 1.711 0.856 2 113 0.6349 0.53189
## soil_root:life_stage 1.276 0.638 2 113 0.4735 0.62405
## precip:life_stage 1.687 1.687 1 113 1.2517 0.26560
## soil_root:precip:life_stage 6.372 3.186 2 113 2.3637 0.09871 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_combin_root_shoot_model, pairwise~life_stage)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## life_stage emmean SE df lower.CL upper.CL
## germinant 2.34 0.217 21.53 1.890 2.79
## seedling 1.16 0.132 5.06 0.817 1.50
##
## Results are averaged over the levels of: soil_root, precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log(mu + 0.001) (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## germinant - seedling 1.18 0.254 6.13 4.661 0.0033
##
## Results are averaged over the levels of: soil_root, precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
emmeans(SG_combin_root_shoot_model, pairwise~life_stage|soil_root|precip)
## $emmeans
## soil_root = L.B, precip = A:
## life_stage emmean SE df lower.CL upper.CL
## germinant 2.058 0.374 92.1 1.316 2.80
## seedling 0.815 0.300 78.7 0.218 1.41
##
## soil_root = S.B, precip = A:
## life_stage emmean SE df lower.CL upper.CL
## germinant 1.523 0.528 109.8 0.477 2.57
## seedling 1.055 0.300 78.7 0.459 1.65
##
## soil_root = L.R, precip = A:
## life_stage emmean SE df lower.CL upper.CL
## germinant 2.099 0.339 86.2 1.426 2.77
## seedling 1.078 0.300 78.7 0.481 1.67
##
## soil_root = L.B, precip = D:
## life_stage emmean SE df lower.CL upper.CL
## germinant 2.106 0.392 98.2 1.327 2.88
## seedling 1.439 0.323 85.6 0.796 2.08
##
## soil_root = S.B, precip = D:
## life_stage emmean SE df lower.CL upper.CL
## germinant 3.667 0.881 100.4 1.918 5.42
## seedling 1.010 0.353 90.9 0.309 1.71
##
## soil_root = L.R, precip = D:
## life_stage emmean SE df lower.CL upper.CL
## germinant 2.588 0.454 97.6 1.687 3.49
## seedling 1.539 0.359 82.8 0.824 2.25
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log(mu + 0.001) (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## soil_root = L.B, precip = A:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 1.243 0.479 58.3 2.595 0.0120
##
## soil_root = S.B, precip = A:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 0.468 0.607 84.7 0.770 0.4432
##
## soil_root = L.R, precip = A:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 1.021 0.452 52.6 2.259 0.0280
##
## soil_root = L.B, precip = D:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 0.667 0.508 63.4 1.312 0.1942
##
## soil_root = S.B, precip = D:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 2.657 0.950 91.5 2.798 0.0063
##
## soil_root = L.R, precip = D:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 1.049 0.579 75.6 1.811 0.0741
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
Formatted Anova table
| Df | Resid.Df | F.value | P.value | |
|---|---|---|---|---|
| soil_root | 2 | 113 | 0.46 | 0.635 |
| precip | 1 | 113 | 6.44 | 0.013 |
| life_stage | 1 | 113 | 23.46 | 0.000 |
| soil_root:precip | 2 | 113 | 0.63 | 0.532 |
| soil_root:life_stage | 2 | 113 | 0.47 | 0.624 |
| precip:life_stage | 1 | 113 | 1.25 | 0.266 |
| soil_root:precip:life_stage | 2 | 113 | 2.36 | 0.099 |
| ### Presence Combined Root:Sho | ot |
Diagnostic Graphs
data_SG_root_shoot_trt_comb_pres=subset(data_SG_root_shoot_trt_comb, root_association =="B")
SG_combin_root_shoot_pres_model= lmer(sqrt(root_shoot)~soil_root*precip*life_stage+(1|block/life_stage), data= data_SG_root_shoot_trt_comb_pres)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(SG_combin_root_shoot_pres_model))
## 251 20
## 35 2
hist(resid(SG_combin_root_shoot_pres_model))
shapiro.test(resid(SG_combin_root_shoot_pres_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_combin_root_shoot_pres_model)
## W = 0.96226, p-value = 0.01852
Raw Statistical output
anova(SG_combin_root_shoot_pres_model)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## soil_root 3.820 3.820 1 72 3.0989 0.0825929 .
## precip 19.930 19.930 1 72 16.1697 0.0001411 ***
## life_stage 33.827 33.827 1 72 27.4445 1.542e-06 ***
## soil_root:precip 7.796 7.796 1 72 6.3251 0.0141377 *
## soil_root:life_stage 5.247 5.247 1 72 4.2571 0.0426929 *
## precip:life_stage 9.546 9.546 1 72 7.7446 0.0068752 **
## soil_root:precip:life_stage 20.164 20.164 1 72 16.3594 0.0001300 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_combin_root_shoot_pres_model, pairwise~precip*life_stage)
## NOTE: Results may be misleading due to involvement in interactions
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## precip life_stage emmean SE df lower.CL upper.CL
## A germinant 2.59 0.311 42.1 1.97 3.22
## D germinant 4.67 0.481 47.4 3.71 5.64
## A seedling 1.84 0.203 14.9 1.41 2.27
## D seedling 2.22 0.230 20.8 1.74 2.70
##
## Results are averaged over the levels of: soil_root
## Degrees-of-freedom method: kenward-roger
## Results are given on the sqrt (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## A,germinant - D,germinant -2.079 0.563 72.0 -3.696 0.0023
## A,germinant - A,seedling 0.750 0.371 14.8 2.022 0.2242
## A,germinant - D,seedling 0.372 0.387 15.4 0.962 0.7723
## D,germinant - A,seedling 2.830 0.522 26.4 5.425 0.0001
## D,germinant - D,seedling 2.451 0.533 25.5 4.601 0.0005
## A,seedling - D,seedling -0.378 0.307 66.9 -1.234 0.6075
##
## Results are averaged over the levels of: soil_root
## Note: contrasts are still on the sqrt scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 4 estimates
emmeans(SG_combin_root_shoot_pres_model, pairwise~life_stage|soil_root|precip)
## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates
## $emmeans
## soil_root = L.B, precip = A:
## life_stage emmean SE df lower.CL upper.CL
## germinant 3.01 0.361 53.5 2.29 3.74
## seedling 1.66 0.287 43.2 1.08 2.23
##
## soil_root = S.B, precip = A:
## life_stage emmean SE df lower.CL upper.CL
## germinant 2.18 0.509 69.0 1.16 3.19
## seedling 2.03 0.287 43.2 1.45 2.61
##
## soil_root = L.B, precip = D:
## life_stage emmean SE df lower.CL upper.CL
## germinant 3.09 0.378 58.5 2.33 3.84
## seedling 2.50 0.310 48.3 1.88 3.12
##
## soil_root = S.B, precip = D:
## life_stage emmean SE df lower.CL upper.CL
## germinant 6.26 0.881 60.4 4.50 8.02
## seedling 1.94 0.339 52.5 1.26 2.62
##
## Degrees-of-freedom method: kenward-roger
## Results are given on the sqrt (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## soil_root = L.B, precip = A:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 1.356 0.461 28.7 2.941 0.0064
##
## soil_root = S.B, precip = A:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 0.145 0.584 46.8 0.248 0.8051
##
## soil_root = L.B, precip = D:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 0.585 0.489 31.9 1.197 0.2401
##
## soil_root = S.B, precip = D:
## contrast estimate SE df t.ratio p.value
## germinant - seedling 4.318 0.944 52.6 4.575 <.0001
##
## Note: contrasts are still on the sqrt scale
## Degrees-of-freedom method: kenward-roger
Formatted Anova table
| Df | Resid.Df | F.value | P.value | |
|---|---|---|---|---|
| soil_root | 1 | 72 | 3.10 | 0.083 |
| precip | 1 | 72 | 16.17 | 0.000 |
| life_stage | 1 | 72 | 27.44 | 0.000 |
| soil_root:precip | 1 | 72 | 6.33 | 0.014 |
| soil_root:life_stage | 1 | 72 | 4.26 | 0.043 |
| precip:life_stage | 1 | 72 | 7.74 | 0.007 |
| soil_root:precip:life_stage | 1 | 72 | 16.36 | 0.000 |
Diagnostic Graphs
data_SG_root_shoot_trt_comb_orig=subset(data_SG_root_shoot_trt_comb, soil_status =="L")
SG_combin_root_shoot_orig_model= lmer(log(root_shoot+0.001)~soil_root*precip*life_stage+(1|block/life_stage), data= data_SG_root_shoot_trt_comb_orig)
## boundary (singular) fit: see ?isSingular
qqPlot(resid(SG_combin_root_shoot_orig_model))
## 531 51
## 70 20
hist(resid(SG_combin_root_shoot_orig_model))
shapiro.test(resid(SG_combin_root_shoot_orig_model))
##
## Shapiro-Wilk normality test
##
## data: resid(SG_combin_root_shoot_orig_model)
## W = 0.97332, p-value = 0.0558
Raw Statistical output
anova(SG_combin_root_shoot_orig_model)
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## soil_root 1.0674 1.0674 1 84 0.8207 0.3675748
## precip 3.5647 3.5647 1 84 2.7406 0.1015573
## life_stage 21.4534 21.4534 1 84 16.4939 0.0001091 ***
## soil_root:precip 0.1050 0.1050 1 84 0.0807 0.7770479
## soil_root:life_stage 0.0350 0.0350 1 84 0.0269 0.8700175
## precip:life_stage 0.4067 0.4067 1 84 0.3127 0.5775090
## soil_root:precip:life_stage 0.4929 0.4929 1 84 0.3790 0.5398262
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(SG_combin_root_shoot_orig_model, pairwise~life_stage)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## life_stage emmean SE df lower.CL upper.CL
## germinant 2.21 0.196 10.4 1.778 2.65
## seedling 1.22 0.158 5.8 0.827 1.61
##
## Results are averaged over the levels of: soil_root, precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log(mu + 0.001) (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## germinant - seedling 0.995 0.252 4.03 3.949 0.0166
##
## Results are averaged over the levels of: soil_root, precip
## Degrees-of-freedom method: kenward-roger
## Results are given on the log (not the response) scale.
Formatted Anova table
| Df | Resid.Df | F.value | P.value | |
|---|---|---|---|---|
| soil_root | 1 | 84 | 0.82 | 0.368 |
| precip | 1 | 84 | 2.74 | 0.102 |
| life_stage | 1 | 84 | 16.49 | 0.000 |
| soil_root:precip | 1 | 84 | 0.08 | 0.777 |
| soil_root:life_stage | 1 | 84 | 0.03 | 0.870 |
| precip:life_stage | 1 | 84 | 0.31 | 0.578 |
| soil_root:precip:life_stage | 1 | 84 | 0.38 | 0.540 |